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NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions Ex 10.2

NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions Ex 10.2 are given here in simple, step-by-step form. NCERT stands for National Council of Educational Research and Training, the body that makes your textbook. An algebraic expression is made using variables like x and y, numbers, and the operations of add, subtract, multiply and divide. Exercise 10.1 was about forming and understanding expressions. Exercise 10.2 teaches you how to find the value of an expression when the value of the variable is given.

This exercise has 10 questions. The idea in each one is the same: wherever the variable appears, replace it with the number given, then work out the answer using the correct order of operations. You will do this for single variables and for expressions with two variables. Every question below is solved in short steps, with the final answer in bold. Students can use this page for homework and revision, parents can use it to check the work at home, and teachers can use it in class. A free printable PDF of these solutions is also available for offline study.

NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions Ex 10.2

Algebraic Expressions

Medium

\begin{array}{l} Get the algebraic expressions in the following cases using \\ variables, constants and arithmetic operations . \\ (i) Subtraction of z from y . \\ (ii) One - half of the sum of numbers x and y . \\ (iii) The number z multiplied by itself . \\ (iv) One - fourth of the product of numbers p and q . \\ (v) Numbersxandyboth squared and added . \\ (vi) Number 5 added to three times the product of \\ numbers m and n . \\ (vii) Product of numbers y and z subtracted from 10. \\ (viii) Sum of numbers a and b subtracted from their \\ product . \end{array}

Algebraic Expressions

Medium

\begin{array}{l} If m = 2, find the value of : \\ (i) m - 2 (ii) 3 m - 5 (iii) 9 - 5 m \\ (iv) 3 m^{2} - 2 m - 7 (v) \frac{5 m}{2} - 4 \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Observe the patterns of digits made from line segments \\ of equal length . You will findsuch segmented digits on \\ the display of electronic watches or calculators . \end{array}

If the number of digits of formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. Hoe many segments are required to form 5, 10, 100 digits of the kind 6, 4, 8.

Algebraic Expressions

Medium

\begin{array}{l} Simplify the expression and find its value when a = 5 and \\ b = -3. \\ 2(a^{2} + ab)+3- ab \end{array}

Algebraic Expressions

Medium

What should be the value of a if the value of 2x² +x – a equals to 5, when x = 0?

Algebraic Expressions

Medium

\begin{array}{l} (i) If z = 10, find the value of z^{3} - 3 (z - 10) . \\ (ii) If p = - 10, find the value of p^{2} - 2 p - 100 . \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Simplify these expressions and find their values if x = 3, \\ a = - 1, b = - 2 . \\ (i) 3 x - 5 - x + 9 (ii) 2 - 8 x + 4 x + 4 \\ (iii) 3 a + 5 - 8 a + 1 (iv) 10 - 3 b - 4 - 5 b \\ (v) 2 a - 2 b - 4 - 5 + a \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Simplify the expressions and find the value if x is equal to 2 \\ (i) x + 7 + 4 (x - 5) (ii) 3 (x + 2) + 5 x - 7 \\ (iii) 6 x + 5 (x - 2) (iv) 4 (2 x - 1) + 3 x + 11 \end{array}

Algebraic Expressions

Medium

\begin{array}{l} When a = 0, b = - 1, find the value of the given expressions : \\ (i) 2 a + 2 b (ii) 2 a^{2} + b^{2} + 1 \\ (iii) 2 a^{2} b + 2 {ab}^{2} + ab (iv) a^{2} + ab + 2 \end{array}

Algebraic Expressions

Medium

\begin{array}{l} If a = 2, b = - 2, find the value of : \\ (i) a^{2} + b^{2} (ii) a^{2} + ab + b^{2} (iii) a^{2} - b^{2} \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Find the value of the following expressions, when x = - 1 : \\ (i) 2 x - 7 (ii) - x + 2 (iii) x^{2} + 2 x + 1 \\ (iv) 2 x^{2} - x - 2 \end{array}

Algebraic Expressions

Medium

\begin{array}{l} If p = - 2, find the value of : \\ (i) 4 p + 7 (ii) - 3 p^{2} + 4 p + 7 (iii) - 2 p^{3} - 3 p^{2} + 4 p + 7 \end{array}

Algebraic Expressions

Medium

\begin{array}{l} (a) From the sum of 3 x - y + 11 and - y - 11, subtract 3 x - y - 11 . \\ (b) From the sum of 4 + 3 x and 5 - 4 x + 2 x^{2}, subtract the sum of 3 x^{2} - 5 x and - x^{2} + 2 x + 5 . \end{array}

Algebraic Expressions

Difficult

\begin{array}{l} (i) Identify the terms and their factors in the following \\ expressions . \\ Show the terms and factors by tree diagrams . \\ (a) x - 3 (b) 1 + x + x^{2} (c) y - y^{3} \\ (d) 5 {xy}^{2} + 7 x^{2} y (e) - ab + 2 b^{2} - 3 a^{2} \\ (ii) Identify terms and factors in the expressions given \\ below : \\ (a) - 4 x + 5 (b) - 4 x + 5 y (c) 5 y + 3 y^{2} \\ (d) xy + 2 x^{2} y^{2} (e) pq + q (f) 1.2 ab - 2.4 b + 3.6 a \\ (g) \frac{3}{4} x + \frac{1}{4} (h) 0.1 p^{2} + 0.2 q^{2} \end{array}

Algebraic Expressions

Medium

What should be taken away from 3x² – 4y² + 5xy + 20 to obtain –x² – y² + 6xy + 20?

Algebraic Expressions

Medium

\begin{array}{l} (a) What should be added to x^{2} + xy + y^{2} to obtain 2 x^{2} + 3 xy ? \\ (b) What should be subtracted from 2 a + 8 b + 10 to get - 3 a + 7 b + 16 ? \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Subtract : \\ (i) - 5 y^{2} {fromy}^{2} \\ (ii) 6 xyfrom - 12 xy \\ (iii) (a - b) from (a + b) \\ (iv) a (b - 5) fromb (5 - a) \\ (v) - m^{2} + 5 mnfrom 4 m^{2} - 3 mn + 8 \\ (vi) - x^{2} + 10 x - 5 from 5 x - 10 \\ (vii) 5 a^{2} - 7 ab + 5 b^{2} from 3 ab - 2 a^{2} - 2 b^{2} \\ (viii) 4 pq - 5 q^{2} - 3 p^{2} from 5 p^{2} + 3 q^{2} - pq \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Add : \\ (i) 3 mn, - 5 mn, 8 mn, - 4 mn \\ (ii) t - 8 tz, 3 tz - z, z - t \\ (iii) - 7 mn + 5, 12 mn + 2, 9 mn - 8, - 2 mn - 3 \\ (iv) a + b - 3, b - a + 3, a - b + 3 \\ (v) 14 x + 10 y - 12 xy - 13, 18 - 7 x - 10 y + 8 xy, 4 xy \\ (vi) 5 m - 7 n, 3 n - 4 m + 2, 2 m - 3 mn - 5 \\ (vii) 4 x^{2} y, - 3 {xy}^{2}, - 5 {xy}^{2}, 5 x^{2} y \end{array}

\begin{array}{l} (viii) 3 p^{2} q^{2} - 4 pq + 5, - 10 p^{2} q^{2}, 15 + 9 pq + 7 p^{2} q^{2} \\ (ix) ab - 4 a, 4 b - ab, 4 a - 4 b \\ (x) x^{2} - y^{2} - 1, y^{2} - 1 - x^{2}, 1 - x^{2} - y^{2} \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Simplify combining like terms : \\ (i) 21 b - 32 + 7 b - 20 b \\ (ii) - z^{2} + 13 z^{2} - 5 z + 7 z^{3} - 15 z \\ (iii) p - (p - q) - q - (q - p) \\ (iv) 3 a - 2 b - ab - (a - b + ab) + 3 ab + b - a \\ (v) 5 x^{2} y - 5 x^{2} + 3 {yx}^{2} - 3 y^{2} + x^{2} - y^{2} + 8 {xy}^{2} - 3 y^{2} \\ (vi) (3 y^{2} + 5 y - 4) - (8 y - y^{2} - 4) \end{array}

Algebraic Expressions

Medium

\begin{array}{l} Identify like terms in the following : \\ (a) - {xy}^{2}, - 4 {yx}^{2}, 8 x^{2}, 2 {xy}^{2}, 7 y, - 11 x^{2}, - 100 x, - 11 yx, \\ 20 x^{2} y, - 6 x^{2}, y, 2 xy, 3 x \\ (b) 10 pq, 7 p, 8 q, - p^{2} q^{2}, - 7 qp, - 100 q, - 23, 12 q^{2} p^{2}, \\ - 5 p^{2}, 41, 2405 p, 78 qp, 13 p^{2} q, {qp}^{2}, 701 p^{2} \end{array}

Algebraic Expressions

Medium

\begin{array}{l} State whether a given pair of terms is of like or unlike \\ terms . \\ (i) 1, 100 (ii) - 7 x, 52 x (iii) - 29 x, - 29 y \\ (iv) 14 xy, 42 yx (v) 4 m^{2} p, 4 {mp}^{2} (vi) 12 xz, 12 x^{2} z \end{array}

Algebraic Expressions

Difficult

\begin{array}{l} Classify into monomials, binomials and trinomials . \\ (i) 4 y - 7 z (ii) y^{2} (iii) x + y - xy (iv) 100 \\ (v) ab - a - b (vi) 5 - 3 t (vii) 4 p^{2} q - 4 {pq}^{2} (viii) 7 mn \\ (ix) z^{2} - 3 z + 8 (x) a^{2} + b^{2} (xi) z^{2} + z (xii) 1 + x + x^{2} \end{array}

Algebraic Expressions

Medium

\begin{array}{l} (a) Identify terms which contain x and give the \\ coefficient of x . \\ (i) y^{2} x + y (ii) 13 y^{2} - 8 yx (iii) x + y + 2 \\ (iv) 5 + z + zx (v) 1 + x + xy (vi) 12 {xy}^{2} + 25 \\ (vii) 7 x + {xy}^{2} \\ (b) Identify terms which contain y^{2} and give the \\ coefficient of y^{2} . \\ (i) 8 - {xy}^{2} (ii) 5 y^{2} + 7 x (iii) 2 x^{2} y - 15 {xy}^{2} + 7 y^{2} \end{array}

Algebraic Expressions

Difficult

\begin{array}{l} Identify the numerical coefficients of terms \\ (other than constants) in the following expressions : \\ (i) 5 - 3 t^{2} (ii) 1 + t + t^{2} + t^{3} (iii) x + 2 xy + 3 y \\ (iv) 100 m + 1000 n (v) - p^{2} q^{2} + 7 pq (vi) 1.2 a + 0.8 b \\ (vii) 3.14 r^{2} (viii) 2 (l + b) (ix) 0.1 y + 0.01 y^{2} \end{array}

Algebraic Expressions

Difficult

\begin{array}{l} Identify the numerical coefficients of terms \\ (other than constants) in the following expressions : \\ (i) 5 - 3 t^{2} (ii) 1 + t + t^{2} + t^{3} (iii) x + 2 xy + 3 y \\ (iv) 100 m + 1000 n (v) - p^{2} q^{2} + 7 pq (vi) 1.2 a + 0.8 b \\ (vii) 3.14 r^{2} (viii) 2 (l + b) (ix) 0.1 y + 0.01 y^{2} \end{array}

Algebraic Expressions

Medium

Use the given algebraic expression to complete the table of number patterns.

S.No.	Expression	Terms
S.No.	Expression	1^st	2^nd	3^th	4^th	5^th		10^th		100^th
(i)		1	3	5	7	9	-	19	-	-	-
(ii)		2	5	8	11	-	-	-	-	-	-
(iii)		5	9	13	17	-	-	-	-	-	-
(iv)		27	34	41	48	-	-	-	-	-	-
(v)		2	5	10	17	-	-	-	-	-	-

NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions Ex 10.2

How to Find the Value of an Expression

Substitute means to put the given number in place of the variable. If x = 2, then 3x becomes 3 × 2.
Follow the correct order of operations: do multiplication and division before addition and subtraction.
Be careful with negative numbers. A minus times a minus gives a plus, and a minus times a plus gives a minus.
For a square term like x², multiply the value by itself. If x = 3, then x² = 3 × 3 = 9.

Exercise 10.2 – Questions and Answers

Q1. If m = 2, find the value of:
(i) m − 2 (ii) 3m − 5 (iii) 9 − 5m (iv) 3m² − 2m − 7 (v) (5m)/2 − 4

Answer: Put m = 2 in each expression.

(i) m − 2 = 2 − 2 = 0
(ii) 3m − 5 = 3(2) − 5 = 6 − 5 = 1
(iii) 9 − 5m = 9 − 5(2) = 9 − 10 = −1
(iv) 3m² − 2m − 7 = 3(2²) − 2(2) − 7 = 3(4) − 4 − 7 = 12 − 4 − 7 = 1
(v) (5m)/2 − 4 = (5 × 2)/2 − 4 = 10/2 − 4 = 5 − 4 = 1

Q2. If p = −2, find the value of:
(i) 4p + 7 (ii) −3p² + 4p + 7 (iii) −2p³ − 3p² + 4p + 7

Answer: Put p = −2, and take care with the signs.

(i) 4p + 7 = 4(−2) + 7 = −8 + 7 = −1

(ii) −3p² + 4p + 7
p² = (−2)² = 4
= −3(4) + 4(−2) + 7
= −12 − 8 + 7
= −13

(iii) −2p³ − 3p² + 4p + 7
p³ = (−2)³ = −8 and p² = 4
= −2(−8) − 3(4) + 4(−2) + 7
= 16 − 12 − 8 + 7
= 3

Q3. Find the value of the following expressions, when x = −1:
(i) 2x − 7 (ii) −x + 2 (iii) x² + 2x + 1 (iv) 2x² − x − 2

Answer: Put x = −1.

(i) 2x − 7 = 2(−1) − 7 = −2 − 7 = −9
(ii) −x + 2 = −(−1) + 2 = 1 + 2 = 3
(iii) x² + 2x + 1 = (−1)² + 2(−1) + 1 = 1 − 2 + 1 = 0
(iv) 2x² − x − 2 = 2(−1)² − (−1) − 2 = 2(1) + 1 − 2 = 2 + 1 − 2 = 1

Q4. If a = 2, b = −2, find the value of:
(i) a² + b² (ii) a² + ab + b² (iii) a² − b²

Answer: Put a = 2 and b = −2.

(i) a² + b² = (2)² + (−2)² = 4 + 4 = 8

(ii) a² + ab + b² = (2)² + (2)(−2) + (−2)² = 4 − 4 + 4 = 4

(iii) a² − b² = (2)² − (−2)² = 4 − 4 = 0

Q5. When a = 0, b = −1, find the value of the given expressions:
(i) 2a + 2b (ii) 2a² + b² + 1 (iii) 2a²b + 2ab² + ab (iv) a² + ab + 2

Answer: Put a = 0 and b = −1.

(i) 2a + 2b = 2(0) + 2(−1) = 0 − 2 = −2

(ii) 2a² + b² + 1 = 2(0)² + (−1)² + 1 = 0 + 1 + 1 = 2

(iii) 2a²b + 2ab² + ab
Every term has an a in it, and a = 0, so every term becomes 0.
= 0

(iv) a² + ab + 2 = (0)² + (0)(−1) + 2 = 0 + 0 + 2 = 2

Q6. Simplify the expressions and find the value if x is equal to 2:
(i) x + 7 + 4(x − 5) (ii) 3(x + 2) + 5x − 7 (iii) 6x + 5(x − 2) (iv) 4(2x − 1) + 3x + 11

Answer: First simplify, then put x = 2.

(i) x + 7 + 4(x − 5) = x + 7 + 4x − 20 = 5x − 13
At x = 2: 5(2) − 13 = 10 − 13 = −3

(ii) 3(x + 2) + 5x − 7 = 3x + 6 + 5x − 7 = 8x − 1
At x = 2: 8(2) − 1 = 16 − 1 = 15

(iii) 6x + 5(x − 2) = 6x + 5x − 10 = 11x − 10
At x = 2: 11(2) − 10 = 22 − 10 = 12

(iv) 4(2x − 1) + 3x + 11 = 8x − 4 + 3x + 11 = 11x + 7
At x = 2: 11(2) + 7 = 22 + 7 = 29

Q7. Simplify these expressions and find their values if x = 3, a = −1, b = −2:
(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

Answer: First simplify by collecting like terms, then substitute.

(i) 3x − 5 − x + 9 = 2x + 4
At x = 3: 2(3) + 4 = 6 + 4 = 10

(ii) 2 − 8x + 4x + 4 = 6 − 4x
At x = 3: 6 − 4(3) = 6 − 12 = −6

(iii) 3a + 5 − 8a + 1 = −5a + 6
At a = −1: −5(−1) + 6 = 5 + 6 = 11

(iv) 10 − 3b − 4 − 5b = 6 − 8b
At b = −2: 6 − 8(−2) = 6 + 16 = 22

(v) 2a − 2b − 4 − 5 + a = 3a − 2b − 9
At a = −1, b = −2: 3(−1) − 2(−2) − 9 = −3 + 4 − 9 = −8

Q8. (i) If z = 10, find the value of z³ − 3(z − 10). (ii) If p = −10, find the value of p² − 2p − 100.

Answer:

(i) z³ − 3(z − 10) at z = 10
= 10³ − 3(10 − 10)
= 1000 − 3(0)
= 1000 − 0
= 1000

(ii) p² − 2p − 100 at p = −10
= (−10)² − 2(−10) − 100
= 100 + 20 − 100
= 20

Q9. What should be the value of a if the value of 2x² + x − a equals 5, when x = 0?

Answer:
Put x = 0 in the expression and set it equal to 5.
2x² + x − a = 5
2(0)² + 0 − a = 5
0 + 0 − a = 5
−a = 5
a = −5
Final answer: a = −5.

Q10. Simplify the expression and find its value when a = 5 and b = −3: 2(a² + ab) + 3 − ab.

Answer:
First simplify.
2(a² + ab) + 3 − ab
= 2a² + 2ab + 3 − ab
= 2a² + ab + 3

Now put a = 5 and b = −3.
= 2(5)² + (5)(−3) + 3
= 2(25) − 15 + 3
= 50 − 15 + 3
= 38

NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions Ex 10.2

NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions Ex 10.2

NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions Ex 10.2

How to Find the Value of an Expression

Exercise 10.2 – Questions and Answers

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