NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions - Download PDF

# NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions - Download PDF

Edited By Ravindra Pindel | Updated on Feb 07, 2024 06:13 PM IST

NCERT Solutions for algebraic expressions class 7: An algebraic expression contains variables, numbers, and operations. In this article, you will get NCERT solutions for class 7 maths chapter 12 Algebraic Expressions. All the algebraic expressions are explained in NCERT. In solutions of NCERT for Class 7 Maths chapter 12 Algebraic Expressions, you will get questions related to solving all three types of algebraic expressions. Also, you will learn the addition and subtraction of algebraic expression. There are many problems in the CBSE NCERT solutions for Class 7 Maths chapter 12 Algebraic Expressions which will give more clarity of the concepts. You can also refer to the NCERT syllabus of Class 7 Maths for better understanding. Check NCERT Solutions from Classes 6 to 12 for Science and Math by clicking on the above link. Here you will get NCERT Solutions for Class 7 for Maths Chapter 12 .

This chapter is important for our coming classes. We must practice questions of this chapter and must be able to solve problems very fastly.

## NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions - Important Formulae

Perimeter of Equilateral triangle = 3a, where, a = side length of triangle

Perimeter of a square = 4a, where, a = side length of square

Perimeter of regular pentagon = 5a, where, a = side length of pentagon

Area of square = a2, where, a = side length of square

Area of rectangle = l × b where, l = length and b = breadth

Area of a Triangle = (1/2) ( b) (h), where b = base and h = height

## NCERT Solutions for Maths Chapter 12 Algebraic Expressions Class 7 - Important Points

Variable: A symbol denoted by letters (such as x, y, z, p, q, r, etc.) that can vary, representing an unknown quantity or value.

How Are Expressions Formed:

Algebraic expressions are formed by combining variables and constants using mathematical operations (Addition, Subtraction, Multiplication, Division).

Terms and Factors of An Expression:

Terms are components of expressions formed by combining variables and constants.

The term includes the sign, so we say "added" without specifying addition or subtraction.

In the diagram, factors are shown with dotted lines and terms with continuous lines.

Coefficient: The coefficient is the numerical factor of a term in an expression.

Free download NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions PDF for CBSE Exam.

## NCERT Solutions for Maths Chapter 12 Algebraic Expressions Class 7th Topic 12.2

Answer: $7xy+5$

the above expression is obtained by adding 7xy with 5. Here 7xy is obtained by multiplying 7,x and y

$4 x^2-5x$

the above expression is obtained by subtracting the product of 5 and x from the product of 4,x and x

## NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Topic 12.3

Answer: $8y+3x^{2}$ The terms in the expression are

$8y\ and\ 3x^{2}$

$8y+3x^{2}$ is obtained by adding the product of 8 and y with the product of 3 x and x

the tree diagram for the expression is given below

$7mn-4$ has two terms 7mn and 4 and the expression is obtained by subtracting 4 from the product of 7,m and n. The tree diagram is shown below.

$2x^2y$ has only one term, that is the expression itself.

The expression is formed by multiplying 4 terms 2, x, x and y. The tree diagrams are shown below

Answer: We can write as many expressions we need with 4 terms. Following are a few examples of expression with 4 terms

$\\ a+b+c+d\\ab+bc+cd+ad\\abc+bcd+acd+abcd$

Answer: i) $4x-3y$ has two terms 4x and -3y

the coefficient of x is 4 and the coefficient of y is -3

ii) a+b+5 has 3 terms a,b and a constant that is 5.

the coefficient of a is 1 and b is also 1. Constant terms have no coefficient

iii) 2y+5 has two terms 2y and 5 which is constant.

The coefficient of y is 2. Constant terms have no coefficient

iv) 2xy has only one term which is 2xy and the coefficient of xy is 2

## NCERT Solutions for Maths Chapter 12 Algebraic Expressions Class 7th Topic 12.4

Question:1(i) Group the like terms together from the following:

Answer: The like terms are grouped below

Group 1: $12x$ , $-25x$ , $x$

Group 2: $-25y$ , $12y$ , $y$

Group 3: $12$ , $-25$ , $1$

## NCERT Solutions for Class 7th Math Chapter 12 Algebraic Expressions Topic 12.5 Monomials, Binomials, Trinomials and Polynomials

binomial: a+b, xy+5, 4mn+7

Trinomial: ab+a+b, 5x 2 -x+2, 4pq-3q+5p, 4m-7n+10

Polynomial with 4 terms: ab+a+b-5

## NCERT Solutions for Class 7th Math Chapter 12 Algebraic Expression Exercise 12.1

Subtraction of $z$ from $y$ .

Answer: Subtraction of z from y: $y-z$

One-half of the sum of numbers $x$ and $y$ .

Answer: Sum of numbers x and y = x + y

One half of the sum of numbers x and y

$=\frac{x+y}{2}$

The number $z$ multiplied by itself.

The number $z$ multiplied by itself $=z\times z=z^{2}$

One-fourth of the product of numbers $p$ and $q$ .

Answer: Product of the numbers p and q $= p \times q=pq$

One-fourth of the product of numbers p and q

$=\frac{pq}{4}$

Numbers $x$ and $y$ both squared and added.

Answer: Number x squared = $x^{2}$

Number y squared = $y^{2}$

Numbers x and y both squared and added = $x^{2}+ y^{2}$

Number 5 added to three times the product of numbers $m$ and $n$ .

Answer: Product of numbers m and n $=m\times n=mn$

Number 5 added to three times the product of numbers $m$ and $n$ = $=3\times mn+5=3mn+5$

Product of numbers $y$ and $z$ subtracted from $10$ .

Answer: Product of numbers y and z $=y\times z=yz$

Product of numbers y and z subtracted from 10 $=10-yz$

Sum of numbers $a$ and $b$ subtracted from their product.

Answer: Sum of numbers a and b = a + b

Product of the numbers a and b $=a\times b=ab$

Sum of numbers $a$ and $b$ subtracted from their product $= ab - (a+b) = ab - a - b$ .

Show the terms and factors by tree diagrams. (a) $x-3$

Answer: Expression : x - 3

Terms in the above expression: x and -3

Tree diagram for the given expression

Show the terms and factors by tree diagrams (b) $1+x+x^{2}$

Answer: Expression: $1 + x + x^2$

Tems in the above expression: $1, x \and\ x^2$

Factors of x 2 : x and x

Tree diagram for the given expression

Show the terms and factors by tree diagrams (c) $y-y^{3}$

Answer: Expression: y - y 3

Terms in the above expression: y and -y 3

Factors of -y 3 : -1, y, y and y

Tree diagram for the given expression

Show the terms and factors by tree diagrams. (d) $5xy^{2}+7x^{2}y$

Answer: Expression: 5xy 2 + 7x 2 y

Terms in the above expression: 5xy 2 and 7x 2 y

Factors of 5xy 2 : 5, x, y and y

Factors of 7x 2 y: 7, x, x and y

Tree diagram for the given expression

Show the terms and factors by tree diagrams (e) $-ab+2ab^{2}-3a^{2}$

Expression: -ab + 2ab 2 - 3a 2

Terms in the above expression: -ab, 2ab 2 and -3a 2

Factors of -ab: -1, a and b

Factors of 2ab 2 : 2, a, b and b

Factors of -3a 2 : -1, 3, a and a

Tree diagram for the given expression

Question: 2 (ii) Identify terms and factors in the expressions given below:

(a) $-4x+5$

Terms in the above expression: -4x and 5

Factors of -4x: -1, 4 and x

Factors of 5: 5

Question: 2 (ii) Identify terms and factors in the expressions given below:

(b) $-4x+5y$

Terms in the above expression: -4x and 5y

Factors of -4x: -1, 4 and x

Factors of 5y: 5 and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(c) $5y+3y^{2}$

Answer: Expression: 5y + 3y 2

Terms in the above expression: 5y and 3y 2

Factors of 5y: 5 and y

Factors of 3y 2 : 3, y and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(d) $xy+2x^{2}y^{2}$

Answer: Expression: xy + 2x 2 y 2

Terms in the above expression: xy and 2x 2 y 2

Factors of xy: x and y

Factors of 2x 2 y 2 : 2, x, x, y and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(e) $pq+q$

Tems in the above expression: pq and q

Factors of pq: p and q

Factors of q: q

Question: 2 (ii) Identify terms and factors in the expressions given below:

(f) $1.2 \; ab-2.4\; b+3.6\; a$

Answer: Expression: 1.2ab - 2.4b + 3.6a

Tems in the above expression: 1.2ab, -2.4b and 3.6a

Factors of 1.2ab: 1.2, a and b

Factors of -2.4b: -1, 2.4 and b

Factors of 3.6a: 3.6 and a

Question: 2( ii) Identify terms and factors in the expressions given below:

(g) $\frac{3}{4}x+\frac{1}{4}$

Answer: Expression: $\frac{3}{4}x+\frac{1}{4}$

Terms in the above expression: $\frac{3}{4}x$ and $\frac{1}{4}$

Factors of $\frac{3}{4}x$ : $\frac{3}{4}$ and x

Factors of $\frac{1}{4}$ : $\frac{1}{4}$

Question: 2 (ii) Identify terms and factors in the expressions given below:

(h) $0.1\; p^{2}+0.2\; q^{2}$

Answer: Expression: 0.1p 2 + 0.2q 2

Tems in the above expression:0.1p 2 and 0.2q 2

Factors of 0.1p 2 : 0.1, p and p

Factors of 0.2q 2 : 0.2, q and q

Answer: Expression: 5 - 3t 2

Tems in the above expression: 5 and -3t 2

Coefficient of -3t 2 : -3

Answer: Expression: 1 + t + t 2 + t 3

Terms in the above expression: 1, t, t 2 and t 3

Coefficient of t is 1

Coefficient of t 2 is 1

Coefficient of t 3 : is 1

Answer: Expression: x + 2xy + 3y

Terms in the above expression: x, 2xy and 3y

Coefficient of x: 1

Coefficient of 2xy: 2

Coefficient of 3y: 3

Terms in the above expression: 100m and 1000n

Coefficient of 100m: 100

Coefficient of 1000n: 1000

Answer: Expression: -p 2 q 2 + 7pq

Tems in the above expression: -p 2 q 2 and 7pq

Coefficient of -p 2 q 2 : -1

Coefficient of 7pq: 7

Terms in the above expression: 1.2a and 0.8b

Coefficient of 1.2a: 1.2

Coefficient of 0.8b: 0.8

Terms in the above expression: 3.14r 2

Coefficient of 3.14r 2 is 3.1

Answer: Expression: 2(l + b) = 2l + 2b

Tems in the above expression: 2l and 2b

Coefficient of 2l: 2

Coefficient of 2b: 2

Answer: Expression: 0.1y + 0.01y 2

Tems in the above expression: 0.1y and 0.01y 2

Coefficient of 0.1y is 0.1

Coefficient of 0.01y 2 is 0.01

(i) $y^{2}x+y$

Answer: Expression: y 2 x + y

Terms with x: y 2 x

Coefficient of x in y 2 x: y 2

(ii) $13y^{2}-8yx$

Answer: Expression: 13y 2 - 8yx

Terms with x: -8yx

Coefficient of x in -8yx: -8y

(iii) $x+y+2$

Answer: Expression: x + y + 2

Terms with x: x

Coefficient of x in x: 1

(iv) $5+z+zx$

Answer: Expression: 5 + z + zx

Terms with x: zx

Coefficient of x in zx: z

(v) $1+x+xy$

Answer: Expression: 1 + x + xy

Terms with x: x and xy

Coefficient of x in x: 1

Coefficient of x in xy: y

(vi) $12xy^{2}+25$

Answer: Expression: 12xy 2 + 5

Terms with x: 12xy 2

Coefficient of x in 12xy 2 : 12y 2

(vii) $7x+xy^{2}$

Answer: Expression: 7x + xy 2

Terms with x: 7x and xy 2

Coefficient of x in 7x: 7

Coefficient of x in xy 2 : y 2

Answer: Expression: 8 - xy 2

Terms with y 2 : -xy 2

Coefficient of y 2 in -xy 2 : -x

Answer: Expression: 5y 2 + 7x

Terms with y 2 : 5y 2

Coefficient of y 2 in 5y 2 : 5

(iii) $2x^{2}y-15xy^{2}+7y^{2}$

Answer: Expression: 2x 2 y -15xy 2 + 7y 2

Terms with y 2 : -15xy 2 and 7y 2

Coefficient of y 2 in -15xy 2 : -15x

Coefficient of y 2 in 7y 2 : 7

(i) 4y – 7z

(ii) y 2

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p 2 q – 4pq 2

(viii) 7mn

(ix) z 2 – 3z + 8

(x) a 2 + b 2

(xi) z 2 + z

(xii) 1 + x + x 2

Binomial

(ii) y 2

Monomial

(iii) x + y – xy

Trinomial

(iv) 100

Monomial

(v) ab – a – b

Trinomial

(vi) 5 – 3t

Binomial

(vii) 4p 2 q – 4pq 2

Binomial

(viii) 7mn

Monomial

(ix) z 2 – 3z + 8

Trinomial

(x) a 2 + b 2

Binomial

(xi) z 2 + z

Binomial

(xii) 1 + x + x 2

Trinomial

Answer: (i) $1,100$ are Like terms.

Answer: (ii) $-7x,\frac{5}{2}x$ are Like terms

Answer: Unlike since y and x are unlike terms

Answer: Like terms, since both the terms contain xy and only the coefficient is different

Answer: Unlike since $m^2p \ and \ mp^2$ are different

Answer: Unlike since $xz \ and\ x^2z$ are unlike terms

Question:7(a) Identify like terms in the following:

(i) -xy 2 and 2xy 2

(ii) -4x 2 y and 20x 2 y

(iii) 8x 2 , -11x 2 and -6x 2

(iv) 7y and y

(v) -100x and 3x

(vi) -11yx and 2xy

Question:7(b) Identify like terms in the following:

(i) 10pq, -7qp and 78qp

(ii) 7p and 2405p

(iii) 8q and -100q

(iv) -p 2 q 2 and 12q 2 p 2

(vii) -23 and 41

(viii) -5p 2 and 701p 2

(ix) 13p 2 q and qp 2

## NCERT Solutions for Class 7th Math Chapter 12 Algebraic Expressions Topic 12.6

$m-n,m+n$

Will give the result as follows

$m-n+m+n=2m$

Subtracting

$m-n,m+n$

Will give the result as follows

$m-n-(m+n)=m-n-m-n=-2n$

$mn+5-2,mn+3$

we will get

$mn+5-2+mn+3=2mn+6$

Subtracting

$mn+5-2,mn+3$

We will get

$mn+5-2-(mn+3)=mn+5-2-mn-3=0$

## NCERT Solutions for Chapter 12 Maths Class 7 Algebraic Expression Exercise: 12.2

Question: 1(i) Simplify combining like terms:

Answer: 21b - 32 + 7b -20b

= (21 + 7 - 20)b -32

= 8b - 32

The simplified expression is 8b - 32.

Question:1(ii) Simplify combining like terms:

Answer: $-z^{2}+13z^{2}-5z+7z^{3}-15z$

-z 2 + 13z 2 - 5z + 7z 3 - 15z

= (-1 + 13)z 2 + (-5 - 15)z +7z 3

=12z 2 - 20z + 7z 3

The simplified expression is 12z 2 - 20z + 7z 3

Question:1(iii) Simplify combining like terms:

Answer: p - (p - q) - q - (q - p)

= p - p + q - q - q + p

= p - p + p + q - q -q

= p - q

The simplified expression is p - q.

Question: 1(iv) Simplify combining like terms:

Answer: 3a - 2b - ab - (a - b + ab) + 3ab + b - a

= 3a - 2b - ab - a + b - ab + 3ab + b - a

= (3 - 1 - 1)a + (-2 + 1 +1)b + (-1 - 1 + 3)ab

= a + ab

The simplified expression is a + ab.

Question:1(v) Simplify combining like terms:

Answer: 5x 2 y - 5x 2 + 3yx 2 - 3y 2 + x 2 - y 2 + 8xy 2 - 3y 2

= (5 + 3 )x 2 y + (-5 + 1)x 2 + (-3 - 1 - 3)y 2 + 8xy 2

= 8x 2 y - 4x 2 - 7y 2 + 8xy 2

The simplified expression is 8x 2 y - 4x 2 - 7y 2 + 8xy 2

Question:1(vi) Simplify combining like terms:

Answer: (3y 2 + 5y - 4) - (8y - y 2 - 4)

= 3y 2 + 5y - 4 - 8y + y 2 + 4

= (3 + 1)y 2 + (5 - 8)y - 4 + 4

= 4y 2 - 3y

The simplified expression is 4y 2 - 3y

(i) $3mn,-5mn,8mn,-4mn$

(ii) $t-8tz,3tz-z,z-t$

(iii) $-7mn+5,12mn+2,9mn-8,-2mn-3$

(iv) $a+b-3,b-a+3,a-b+3$

(v) $14x+10y-12xy-13,18-7x-10y+8xy,4xy$

(vi) $5m-7n,3n-4m+2,2m-3mn-5$

(vii) $4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y$

(viii) $3p^{2}q^{2}-4pq+5,-10 p^{2}q^{2},15+9pq+7p^{2}q^{2}$

(ix) $ab-4a,4b-ab,4a-4b$

(x) $x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}$

$\\(i) 3mn + (-5mn) + 8mn + (-4mn)\\ = (3 - 5 + 8 - 4)mn\\ = 2mn$

$\\(ii) t - 8tz + (3tz - z) + (z - t)\\ = t - 8tz + 3tz - z + z - t\\ = (1 - 1)t + (-8 + 3)tz + (-1 + 1)z\\ = -5tz$

$\\(iii) -7mn + 5 + (12mn + 2) + (9mn - 8) + (-2mn - 3)\\ = -7mn + 5 + 12mn + 2 + 9mn - 8 - 2mn - 3 \\= (-7 + 12 + 9 - 2)mn + 5 + 2 - 8 - 3 \\= 12mn - 4$

$\\(iv) a + b - 3 + (b - a + 3) + (a - b + 3)\\ \\= a + b - 3 + b - a + 3 + a - b + 3 \\= (1 - 1 + 1)a + (1 + 1 -1)b - 3 + 3 + 3 \\= a + b + 3$

$\\(v) 14x + 10y - 12xy - 13 + (18 - 7x - 10y + 8xy) + 4xy\\ = 14x + 10y - 12xy - 13 + 18 - 7x - 10y + 8xy + 4xy \\= (14 -7)x + (10 - 10)y + (-12 + 8 + 4)xy - 13 + 18 \\= 7x + 5$

$\\(vi) 5m - 7n + (3n - 4m + 2) + (2m - 3mn - 5) \\= 5m - 7n + 3n - 4m + 2 + 2m - 3mn - 5 \\= (5 - 4 + 2)m + (-7 + 3)n + 2 - 5 - 3mn \\= 3m - 4n - 3mn - 3$

$\\(vii) 4x^2y - 3xy^2 - 5xy^2 + 5x^2y\\ \\= (4 + 5)x^2y + (-3 - 5)xy^2 \\= 9x^2y - 8xy^2$

$\\(viii) 3p^2q^2 - 4pq + 5 + (-10p^2q^2) + (15 + 9pq + 7p^2q^2) \\= 3p^2q^2 - 4pq + 5 - 10p^2q^2 + 15 + 9pq + 7p^2q^2 \\= (3 - 10 + 7)p^2q^2 + (-4 + 9)pq + 5 + 15 \\= 5pq + 20$

$\\(ix) ab - 4a + (4b - ab) + (4a - 4b) \\= ab - 4a + 4b - ab + 4a - 4b \\= (1 - 1)ab + (-4 + 4)a + (4 - 4)b \\=0$

$\\(x)\ x^2 - y^2 - 1 + (y^2 - 1 - x^2) + (1 - x^2 - y^2) \\= (1 - 1 - 1)x^2 + (-1 + 1 - 1)y^2 - 1 - 1 + 1 \\= -x^2 - y^2 - 1$

Question:3 Subtract:

(i) $-5y^{2}$ from $y^{2}$

(ii) $6xy$ from $-12xy$

(iii) $(a-b)$ from $(a+b)$

(iv) $a(b-5)$ from $b(5-a)$

(v) $-m^{2}+5mn$ from $4m^{2}-3mn+8$

(vi) $-x^{2}+10x-5$ from $5x-10$

(vii) $5a^{2}-7ab+5b^{2}$ from $3ab-2a^{2}-2b^{2}$

(viii) $4pq-5q^{2}-3p^{2}$ from $5p^{2}+3q^{2}-pq$

Answer: The given terms are subtracted as follows

(i)

$\\ y^2 - (-5y^2) \\= y^2 + 5y^2 \\= 6y^2$

(ii)

$\\ -12xy - 6xy\\ = -18xy$

(iii)

$\\(a+b)-(a-b)\\ =a+b-a+b =2b$

(iv)

$\\ b(5 - a) - a(b - 5) \\= 5b - ab - (ab - 5a) \\= 5b - ab - ab + 5a \\= 5b - 2ab + 5a$

(v)

$\\4m^2 - 3mn + 8 - (-m^2 + 5mn) \\= 4m^2 - 3mn + 8 + m^2 - 5mn \\= (4 + 1)m^2 + (-3 - 5)mn + 8 \\= 5m^2 - 8mn + 8$

(vi)

$\\ 5x - 10 - (-x^2 + 10x - 5) \\= 5x - 10 + x^2 - 10x + 5 \\= x^2 + (5 - 10)x - 10 + 5 \\= x^2 - 5x - 5$

(vii)

$\\ 3ab - 2a^2 - 2b^2 - (5a^2 - 7ab + 5b^2) \\= 3ab - 2a^2 - 2b^2 - 5a^2 + 7ab - 5b^2 \\= (3 + 7)ab + (-2 -5)a^2 + (-2 - 5)b^2 \\= 10ab - 7a^2 - 7b^2$
(viii)

$\\ 5p^2 + 3q^2 - pq - (4pq - 5q^2 - 3p^2) \\= 5p^2 + 3q^2 - pq - 4pq + 5q^2 + 3p^2 \\= (5 + 3) p^2 + (3 + 5)q^2 + (-1 - 4)pq \\= 8p^2 + 8q^2 - 5pq$

Answer: Let the term be a which must be added to x 2 + xy + y 2 to obtain 2x 2 + 3xy

$\\a + x^2 + xy + y^2 = 2x^2 + 3xy \\a = 2x^2 + 3xy - (x^2 + xy + y^2) \\a = (2-1)x^2 + (3 - 1)xy -y^2 \\a = x^2 + 2xy - y^2$

x 2 + 2xy - y 2 should be added to x 2 + xy + y 2 to obtain 2x 2 + 3xy

Answer: Let the term be c which must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

$\\2a + 8b + 10 - c = -3a + 7b + 16 \\c = 2a + 8b + 10 - (-3a + 7b + 16) \\c = 2a + 8b + 10 + 3a - 7b - 16 \\c = (2 + 3)a + (8 - 7)b + 10 - 16 \\c = 5a + b - 6$

5a + b - 6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

Answer: Let the term be a which must be taken away from 3x 2 - 4y 2 + 5xy + 20 to obtain -x 2 - y 2 + 6xy + 20

$\\3x^2 - 4y^2 + 5xy + 20 - a = -x^2 - y^2 + 6xy + 20 \\a = 3x^2 - 4y^2 + 5xy + 20 - ( -x^2 - y^2 + 6xy + 20 ) \\a = 3x^2 - 4y^2 + 5xy + 20 + x^2 + y^2 - 6xy - 20 \\a = ( 3 + 1 )x^2 + ( -4 + 1 )y^2 + ( 5 - 6 )xy + 20 - 20 \\a = 4x^2 - 3y^2 - xy$

4x 2 - 3y 2 - xy must be taken away from 3x 2 - 4y 2 + 5xy + 20 to obtain -x 2 - y 2 + 6xy + 20

$\\( 3x - y + 11 + ( - y - 11 ) ) - ( 3x - y - 11 ) \\= 3x - y + 11 - y - 11 - 3x + y + 11 \\= ( 3 - 3 )x + ( -1 - 1 + 1)y + 11 - 11 + 11 \\= -y + 11$

On subtracting 3x - y - 11 from the sum of 3x - y + 11 and -y - 11 we get -y + 11

$\\( 4 + 3x + ( 5 - 4x + 2x^2) ) - ( 3x^2 - 5x + ( -x^2 + 2x + 5) \\= (4 + 3x + 5 - 4x + 2x^2 ) - ( 3x^2 - 5x -x2 + 2x + 5) \\= 4 + 3x + 5 - 4x + 2x^2 - 3x^2 + 5x + x^2 - 2x - 5 \\=4 + 5 - 5 + ( 3 - 4 + 5 - 2 )x + ( 2 - 3 + 1 )x^2 \\=4 + 2x$

On subtracting the sum of $3x^{2}-5x$ and $-x^{2}+2x+5$ from the sum of $4+3x$ and $5-4x+2x^{2}$ we get $4+2x$

## NCERT Solutions for Chapter 12 Maths Class 7th Algebraic Expression Exercise 12.3

= 2 - 2

= 0

If m = 2 the value of m - 2 = 0

$\\3m - 5 \\= 3 \times 2 - 5 \\= 6 - 5 \\= 1$

If m = 2 the value of 3m - 5 = 1

$\\9 - 5m \\= 9 - 5 \times 2 \\= 9 - 10 \\= -1$

If m = 2 the value of 9 - 5m = -1

$\\3m^2 - 2m - 7 \\= 3 \times 2^2 - 2 \times 2 - 7 \\= 12 - 4 - 7 \\= 1$

If m = 2 the value of 3m 2 - 2m - 7 = 1

$\frac{5m}{2}-4$

$=\frac{5\times 2}{2}-4$

= 5 - 4

= 1

If m = 2 the value of $\frac{5m}{2}-4 = 1$

$\\4p + 7 \\= 4 \times ( -2 ) + 7 \\= -8 + 7 \\= -1$

If p = -2 the value of 4p + 7 = -1

$\\-3p^2 + 4p + 7 \\= -3 x ( -2 )^2 + 4 x ( -2 ) + 7 \\= -12 - 8 + 7 \\= -13$

If p = -2 the value of -3p 2 + 4p + 7 = -13

$\\-2p3 - 3p2 + 4p + 7 \\= - 2 \times ( -2)^3 - 3 \times ( -2 )^2 + 4 \times ( -2 ) + 7 \\= 16 - 12 - 8 + 7 \\= 3$

If p = -2 the value of -2p 3 - 3p 2 + 4p + 7 = 3

$\\2x - 7 \\= 2 \times ( -1 ) - 7 \\= -2 - 7 \\= -9$

If x = -1 the value of 2x - 7 = -9

Question: 3(ii) Find the value of the following expressions, when

-x + 2

= -( -1 ) + 2

= 1 + 2

= 3

If x = -1 the value of -x + 2 = 3

$\\x^2 + 2x + 1 \\= ( -1 )^2 + 2 \times ( -1 ) + 1 \\= 1 - 2 + 2 \\= 0$

If x = -1 the value of x 2 + 2x + 1 = 0

$\\2x^2 - x - 2 \\= 2\times ( -1 )^2 - ( -1 ) - 2 \\ = 2 + 1 - 2 \\= 1$

So the value at x=-1 is 1

a 2 + b 2

= ( 2 ) 2 + ( -2 ) 2

= 4 + 4

= 8

If a = 2 and b = -2 the value of a 2 + b 2 = 8

$\\a^2 + ab + b^2 \\= 2^2 + 2 \times ( -2 ) + ( -2 )^2 \\= 4 - 4 + 4 \\= 4$

If a = 2 and b = -2 the value of a 2 + ab + b 2 = 4

a 2 - b 2

= 2 2 - ( -2 ) 2

= 4 - 4

= 0

If a = 2 and b = -2 the value of a 2 - b 2 = 0

$\\2a + 2b \\= 2 \times 0 + 2 \times ( -1 ) \\= 0 - 2 \\= -2$

When a = 0 and b = -1 the value of the given expression 2a + 2b = -2

$\\2a^2 + b^2 + 1 \\= 2 \times 0^2 + ( -1 )2 + 1 \\= 0 + 1 + 1 \\= 2$

When a = 0 and b = -1 the value of the given expression 2a 2 + b 2 + 1 = 2

$\\2a^2b + 2ab^2 + ab \\= 2 \times 0^2 \times ( -1 ) + 2 \times 0 \times ( -1 )^2 + 0 \times ( -1 )\\ = 0 + 0 + 0 \\= 0$

When a = 0 and b = -1 the value of the given expression 2a 2 b + 2ab 2 + ab = 0

$\\a^2 + ab + 2 \\= 0^2 + 0 \times ( -1 ) + 2 \\= 0 + 0 + 2 \\= 2$

When a = 0 and b = -1 the value of the given expression a 2 + ab + 2 = 2

$\\x + 7 + 4( x - 5 ) \\= x + 7 + 4x - 20 \\= 5x - 13 \\= 5 \times 2 - 13 \\= 10 - 13 \\= -3$

If x is equal to 2 the value of x + 7 + 4( x - 5 ) = -3

$\\3( x + 2 ) + 5x - 7 \\= 3x + 6 + 5x - 7 \\= 8x - 1 \\= 8 \times (2) - 1 \\= 16 - 1 \\= 15$

If x is equal to 2 the value of 3( x + 2 ) + 5x - 7 = 15

$\\6x + 5( x - 2 ) \\= 6x + 5x - 10 \\= 11x - 10 \\= 11 \times 2 - 10 \\= 22 - 10 \\= 12$

If x is equal to 2 the value of 6x + 5( x - 2 ) = 12

$\\4( 2x - 1 ) + 3x + 11 \\= 8x - 4 + 3x + 11 \\= 11x + 7 \\= 11 \times 2 + 7 \\= 22 + 7 \\= 29$

If x is equal to 2 the value of 4( 2x - 1 ) + 3x + 11 = 29

(i) $3x-5-x+9$

(ii) $2-8x+4x+4$

(iii) $3a+5-8a+1$

(iv) $10-3b-4-5b$

(v) $2a-2b-4-5+a$

The expression is simplified as follows and also obtained their values

(i)

$\\ 3x - 5 - x + 9 \\= 2x + 4 \\= 2 \times 3 + 4 \\= 10$

(ii)

$\\ 2 - 8x + 4x + 4 \\= 6 - 4x \\= 6 - 4 \times 3 \\= -6$

(iii)

$\\3a + 5 - 8a + 1 \\= -5a + 6 \\= -5 \times ( -1 ) + 6 \\= 5 + 6 \\=11$

(iv)

$\\10 - 3b - 4 - 5b \\= 6 - 8b \\= 6 - 8 \times ( -2 ) \\= 6 + 16 \\= 22$

(v)

$\\2a - 2b - 4 - 5 + a \\= 3a - 2b - 9 \\= 3 \times ( -1 ) - 2 \times ( -2 ) - 9 \\= -3 + 4 - 9 \\= -8$

$\\z^3 - 3( z - 10 ) \\= z^3 - 3z + 30 \\= 10^3 - 3 \times 10 + 30 \\= 1000 - 30 + 30 \\= 1000$

If z = 10 the value of z 3 - 3( z - 10 ) = 1000

Question: 8 (ii) If $p=-10,$ find the value of

$\\p^2 - 2p - 100 \\= ( -10 )^2 - 2 \times ( -10 ) - 100 \\= 100 + 20 - 100 \\= 20$

If p = -10 the value of p 2 - 2p - 100 = 20

$\\2x^2 + x - a = 5 \\2 \times 0^2 + 0 - a = 5 \\-a = 5 \\a = -5$

Therefore for a = -5 when the value of x=0

$\\2( a^2 + ab ) + 3 - ab \\= 2a^2 + 2ab + 3 - ab \\= 2a^2 + ab + 3 \\= 2 \times 5^2 + 5 \times ( -3 ) + 3 \\= 50 - 15 + 3 \\= 38$

When a = 5 and b = -3 the value 2( a 2 + ab ) + 3 - ab = 38

## NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expression Exercise 12.4

The number of segments required to form n of each digits shown above are 5n + 1, 3n + 1 and 5n + 2

When n = 5

$\\5n + 1 = 5 \times 5 + 1 = 26 \\3n + 1 = 3 \times 5 + 1 = 16 \\5n + 2 = 5 \times 5 + 2 = 27$

When n = 10

$\\5n + 1 = 5 \times 10 + 1 = 51 \\3n + 1 = 3 \times 10+ 1 = 31 \\5n + 2 = 5 \times 10 + 2 = 52$

When n = 100

$\\5n + 1 = 5 \times 100 + 1 = 501 \\3n + 1 = 3 \times 100+ 1 = 301 \\5n + 2 = 5 \times 100 + 2 = 502$

Answer: Below you can find the table of number patterns:

## Algebraic Expressions Class 7 Chapter 12-Topics

• How Are Expressions Formed?
• Terms Of An Expression
• Like And Unlike Terms
• Monomials, Binomials, Trinomials And Polynomials
• Addition And Subtraction Of Algebraic Expressions
• Finding The Value Of An Expression
• Using Algebraic Expressions – Formulas And Rules

#### NCERT Solutions for Class 7 Maths Chapter Wise

 Chapter No. Chapter Name Chapter 1 Integers Chapter 2 Fractions and Decimals Chapter 3 Data Handling Chapter 4 Simple Equations Chapter 5 Lines and Angles Chapter 6 The Triangle and its Properties Chapter 7 Congruence of Triangles Chapter 8 Comparing quantities Chapter 9 Rational Numbers Chapter 10 Practical Geometry Chapter 11 Perimeter and Area Chapter 12 Algebraic Expressions Chapter 13 Exponents and Powers Chapter 14 Symmetry Chapter 15 Visualising Solid Shapes

#### NCERT Solutions for Class 7 Subject Wise

 NCERT Solutions for Class 7 Maths

#### Benefits of NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

• You will learn to simplify and solve algebraic expressions in this chapter.
• You will also learn the addition and subtraction of algebraic expressions which is helpful in making the expression simpler.
• There are many questions given below every topic to give you conceptual clarity. In NCERT solutions for Class 7 Maths chapter 12 Algebraic Expressions, you will get solutions to these practice questions also.
• You should practice all the NCERT questions including examples. If you facing difficulties in doing so, you can take help from these solutions.

Happy learning!!!

Also Check NCERT Books and NCERT Syllabus here:

1. How many terms are there in the expression 2y+5?

There are 2 terms in this expression. To know what are terms and other concepts students can download algebraic expressions class 7 pdf and study both online and offline mode. After practicing these concepts you have confidence that will help you during the exam and lead to score well.

2. How many exercises in NCERT Class 7 Maths Chapter 12?

There are 4 exercises in NCERT Class 7 Mathematics Chapter 12

NCERT Maths Chapter 12 Algebraic Expression Class 7 Exercise 12.1 - 7 questions

NCERT Maths Chapter 12 Algebraic Expression Class 7 Exercise 12.2 - 6 questions

Class 7 Maths Chapter 12 Algebraic Expression Exercise 12.3 - 10 questions

Class 7 Maths Chapter 12 Algebraic Expression Exercise 12.4 - 2 questions

3. What are the topics covered in NCERT Class 7 Chapter 12?

Here are the topics covered in NCERT Maths Class 7 Chapter 12

•  How Are Expressions Formed?
•   Terms Of An Expression
•    Like And Unlike Terms
•    Monomials, Binomials, Trinomials And Polynomials
•    Addition And Subtraction Of Algebraic Expressions
•    Finding The Value Of An Expression
•    Using Algebraic Expressions – Formulas And Rules

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