### NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.2

## Introduction:

NCERT Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.1

NCERT Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.2

**Class 7 Maths Algebraic Expression Exercise 10.2 (Page-168)**

**Q1. **If m = 2, find the value of:

(i) m - 2

(ii) 3m - 5

(iii) 9 - 5m

(iv) 3m² - 2m - 7

(v) \(\displaystyle \frac{{5m}}{2}\) - 4

**Solution: **

(i) putting value of m =2

= 2 - 2

= 0

(ii) putting value of m =2

= 3(2) - 5

= 6 - 5

= 1

(iii) putting value of m =2

= 9 - 5(2)

= 9 - 10

= -1

(iv) putting value of m =2

= 3(2)² - 2(2) - 7

= 3 (4) - 4 - 7

= 12 - 11

= 1

(v) putting value of m =2

= \(\displaystyle \frac{{5(2)}}{2}\) - 4

= \(\displaystyle \frac{{10}}{2}\) - 4

= 5 - 4

= 1

**Q2. **If p = -2, find the value of :

(i) 4p + 7

(ii) -3p² + 4p + 7

(iii) - 2p³ - 3p² + 4p+ 7

**Solution: **

(i) putting the value of p = -2

= 4(-2) + 7

= -8 + 7

= -1

(ii) putting the value of p = -2

= -3(-2)² + 4(-2) + 7

= -3( 4) + (-8) + 7

= - 12 - 8 + 7

= - 20 + 7

= - 13

(iii) putting the value of p = -2

= - 2(-2)³ - 3(-2)² + 4(-2) + 7

= -2 (-8) - 3 (4) + (-8) + 7

= 16 - 12 - 8 + 7

= 16 - 20 + 7

= -4 + 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

**Solution: **

(i) putting the value of x = -1

= 2(-1) - 7

= -2 - 7

= -9

(ii) putting the value of x = -1

= - (-1) + 2

= 1 + 2

= 3

(iii) putting the value of x = -1

= (-1)² + 2(-1) + 1

= 1 - 2 +1

= -1 +1

= 0

(iv) putting the value of x = -1

= 2(-1)² - (-1) -2

= 2(1) + 1 - 2

= 2 + 1 -2

= 3 - 2

= 1

**Q4. **If a = 2, b= -2, find the value of:

(i) a² + b²

(ii) a² + ab + b²

(iii) a² - b²

**Solution: **

(i) Putting value of a = 2 and b= -2

= (2)² + (-2)²

= 4 + 4

= 8

(ii) Putting value of a = 2 and b= -2

= (2)² + (2)(-2) + (-2)²

= 4 + (-4) + 4

= 4 - 4 + 4

= 0 + 4

= 4

(iii) Putting value of a = 2 and b= -2

= (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

**Solution: **

(i) Putting value of a = 0 and b= -1

= 2 (0) + 2(-1)

= 0 - 2

= -2

(ii) Putting value of a = 0 and b= -1

= 2(0)² + (-1)² + 1

= 0 + 1 + 1

= 2

(iii) Putting value of a = 0 and b= -1

= 2(0)²(-1) + 2(0)(-1)² + (0)(-1)

= 2 (0) + 2(0) +(0)

= 0 +0+0

= 0

(iv) Putting value of a = 0 and b= -1

= (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

**Solution: **

(i) putting the value of x = 2

= (2)+ 7 + 4(2-5)

= 9 + 8 - 20

= 17 - 20

= -3

(ii)putting the value of x = 2

= 3(2+2) + 5(2) - 7

= 3(4) + 10 - 7

= 12 + 10 - 7

= 22 - 7

= 15

(iii)putting the value of x = 2

= 6(2) + 5(2 - 2)

= 12 + 5(0)

= 12 + 0

= 12

(iv)putting the value of x = 2

= 4( 2x - 1) + 3x + 11

= 8x - 4 + 3x + 11

= 8(2) - 4 + 3(2) + 11

= 16 - 4 + 6 + 11

= 12 + 17

= 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

**Solution:**

(i) Putting value of x= 3

= 3x - 5 - x + 9

= 3x -x -5 + 9

= 2x + 4

= 2(3) + 4

= 6 + 4

= 10

(ii) Putting value of x= 3

= 2 - 8x + 4x + 4

= -4x + 2+ 4

= - 4x + 6

= -4(3) + 6

= - 12 + 6

= - 6

(iii) Putting value of a = -1

= 3a + 5 - 8a + 1

= 3a - 8a +5 + 1

= -5a + 6

= - 5(-1) + 6

= 5 + 6

= 11

(iv) Putting value of b= -2

= 10 - 3b - 4 -5b

= - 3b - 5b -4 + 10

= -8b +6

= - 8 (-2) + 6

= 16 + 6

= 22

(v) Putting value of a = -1, b= -2

= 2a - 2b - 4 -5 + a

= 2a + a -2b -9

= 3a - 2b -9

= 3(-1) -2(-2) -9

=-3 + 4 - 9

= 1 - 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

**Solution: **

(i) Putting value of z = 10

= z³ - 3(z- 10)

= z³ - 3z - 30

= (10)³ - 3(10) - 10

= 1000 - 30 - 30

= 1000 -0

= 1000

(ii) Putting value of p = -10

= p² -2p -100

= (-10)² - 2(-10) - 100

= 100 + 20 - 100

= 120 - 100

= 20

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

**Solution: **2x² + x - a = 5

putting value of x = 0

2(0)² + (0) - a = 5

0 + 0 -a = 5

-a = 5

a = -5

So, the value of x is equals to 5.

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

**Solution: **2(a² + ab) +3 -ab

= 2a² + 2ab + 3 -ab

= 2a² + 2ab -ab + 3

= 2a² + ab + 3

putting the value of a = 5 and b= -3

= 2 (5)² + (5× -3) + 3

= 2 (25) - 15 + 3

= 50 - 12

= 38