NCERT Solutions Class 7th Math Chapter 10 Algebraic Expressions Examples

October 20, 2023

NCERT Solutions Class 7 Math Chapter 10 Algebraic Expressions

Textbook	NCERT
Class	7th
Subject	Math
Chapter	10^th
Chapter Name	Algebraic Expressions
Category	Class 7th Math Solutions
Medium	English
Source	Last Doubt

NCERT Solutions Class 7 Math Chapter 10 Algebraic Expressions

Chapter – 10

Algebraic Expressions

Example

Example. 1 Identify, in the following expressions, terms which are
not constants. Give their numerical coefficients:
xy+4, 13-y’, 13-y+5y’, 4p’q-3pq+5Solution-

S. No.	Expression	Term (which is not a Constant)	Numerical Coefficient
(i)	xy+4	xy	1
(ii)	13-y²	– y²	-1
(iii)	13-y+5y²	– y 5y2	-1 5
(iv)	4p2q-3pq²+5	4p2q -3pq²	4 -3

Example.2 (a) What are the coefficients of x in the following expressions?
4x-3y, 8-x+y, yx-y, 2z-5xz(b) What are the coefficients of y in the following expressions?
4x-3y, 8+ yz, yz²+5, my +mSolution-
(a) In each expression we look for a term with x as a factor. The remaining part of that
term is the coefficient of x.

S. No.	Expression	Term with Factor x	Coefficient of x
(i)	4x-3y	4x	4
(ii)	8-x+y	-x	-1
(iii)	yz²+5	yz²	z²
(iv)	2z -5xz	– 5xz	– 5z

(b) The method is similar to that in (a) above.

S. No.	Expression	Term with Factorx	Coefficient of y
(i)	4x-3y	-3y	-3
(ii)	8+ yz	yz	z
(iii)	yz²+5	yz²	z²
(iv)	my + m	my	m

Example. 3 State with reasons, which of the following pairs of terms are of like
terms and which are of unlike terms:
(i) 7x, 12y
(ii) 15x, -21x
(iii) -4ab, 7ba
(iv) 3xy, 3x
(v) 6xy2, 9xy
(vi) pq, -4pq
(vii) mn², 10mnSolution-

S. No	Pair	Factors	Algebraic factors same or different	Like/ Unlike terms	Remarks
(i)	7x 12y	7, x 12, y}	Different	Unlike	The variables in the terms are different.
(ii)	15.x -21x	15, x -21, x ]	Same	Like
(iii)	-4ab 7 ba	-4, a, b 7, a, b}	Same	Like	Remember ab = ba
(iv)	3xy 3x	3, х, у 3, x}	Different	Unlike	The variable y is only in one term.
(v)	6xy2 9x2y	6, x, y, y 9, x, x, y	Different	Unlike	The variables in the two terms match, but their powers do not match.
(vi)	pq2-4pq2	1, p. q. q -4p, q, q}	Same	Like	Note, numerical factor 1 is not shown

Following simple steps will help you to decide whether the given terms are like
or unlike terms:

(i) Ignore the numerical coefficients. Concentrate on the algebraic part of t
terms.

(ii) Check the variables in the terms. They must be the same.

(iii) Next, check the powers of each variable in the terms. They must be the same.

Note that in deciding like terms, two things do not matter (1) the numerical
coefficients of the terms and (2) the order in which the variables are multiplied in the
terms.

Example. 4 Find the values of the following expressions for x=2.
(i) x + 4
(ii) 4x-3
(iii) 19-5×2
(iv) 100-10x³Solution- Putting .x=2(i) Inx +4, we get the value of x + 4, i.e.,
x+4=2+4= 6(ii) In 4x-3, we get
4x-3=(4×2)-3=8-3=5(iii) In 19-5x², we get
19–5r=19 – (5 x 2²) = 19 – (5 x 4) = 19 – 20 =-1(iv) In 100-10x³, we get
100-10x³ 100-(10×2³) = 100-(10 x 8) (Note 2³ = 8)
= 100-80 = 20

Example. 5 Find the value of the following expressions when n = -2.
(i) 5n-2 (ii) 5n²+5n-2 (iii) n³+5n²+5n-2

Solution-

(i) Putting the value of n=-2, in 5n-2, we get,
5(-2)-2-10-2=-12

(ii) In 5n²+5n-2, we have,
for n=-2, 5n-2=-12

and 5n²=5x (-2)²=5×4=20
Combining,
5n²+5n-2=20-12=8
[as (-2)²=4]

(iii) Now, for n = -2,
5n²+5n-28 and
n³=(-2)3=(-2)x(-2)x(-2)=-8
Combining,
n³ +5n²+5n-2=-8+8=0

We shall now consider expressions of two variables, for example, x+y, xy. To work
out the numerical value of an expression of two variables, we need to give the values of
both variables. For example, the value of (x + y), for x=3 and y = 5, is 3+5=8.

Example. 6 Find the value of the following expressions for a = 3, b=2.
(i) a+b
(ii) 7a-4b
(iii) a²+2ab+b²
(iv) a³-b3Solution- Substituting a = 3 and b=2 in
(i) a + b, we get
a+b=3+2=5(ii) 7a-4b, we get
7a-4b=7×3-4×2=21-8=13.(iii) a²+2ab+b², we get
a²+2ab+b² = 3²+2×3×2+2²=9+ 2 x 6 + 4 = 9+12+4=25(iv) a-b’, we get
a³-b³=33-23=3x3x3-2x2x2=9×3-4×2=27-8=19