# RS Aggarwal Class 8 Math Sixth Chapter Operation on Algebric Expressions Exercise 6E Solution

## EXERCISE 6E

### OBJECTIVE QUESTIONS

#### Tick (√) the correct answer in each of the following:

(1) The sum of (6a + 4b – c + 3), (2b – 3c + 4), (11b – 7a + 2c – 1) and (2c – 5a – 6) is

Ans: (c) (- 6a + 17b)

Solution: (6a + 4b – c + 3) + (2b – 3c + 4) + (11b – 7a + 2c – 1) + (2c – 5a – 6)

= 6a + 4b – c + 3 + 2b – 3c + 4 + 11b – 7a + 2c – 1 + 2c – 5a – 6

= – 6a + 17b

(2) (3q + 7p2 – 2r3 + 4) – (4p2 – 2q + 7r3 – 3) =?

Ans: (d) (3p2 + 5q – 9r3 + 7)

Solution: 3q + 7p2 – 2r3 + 4 – 4p2 + 2q – 7r3 + 3

= 3p2 + 5q – 9r3 + 7

(3) (x + 5) (x – 3) =?

= x2 + 5x – 3x – 15

= x2 + 2x – 15

Ans: (d)

(4) (2x+ 3) (3x – 1)

= 6x2 + 9x – 2x – 3

= 6x2 + 7x – 3

Ans: (b)

(5) (x + 4) (x + 4)

= x2 + 4x + 4x + 16

= x2 + 8x + 16

Ans: (c)

(6) (x – 6) (x – 6)

= x2 – 6x – 6x + 36

= x2 – 12x + 36

Ans: (d)

(7) (2x + 5) (2x – 5)

= 4x2 + 10x – 10x – 25

= (4x2 – 25)

Ans: (b)

(8) 8a2b3 ÷ (- 2ab)

Ans: (c)

(9) (2x2 + 3x + 1) ÷ (x + 1)

= 2x + 1

Ans: (b)

(10) (x2 – 4x + 4) ÷ (x – 2)

= (x – 2)

Ans: (a)

(11) (a + 1) (a – 1) (a2 + 1)

= [(a)2 – (1)2] (a2 + 1)

= (a2 – 1) (a2 + 1)

= (a2)2 – (1)2

= (a4 – 1)

Ans: (c)

(15) (82)2 – (18)2

= (80 + 2)2 – (20 – 2)2

= [(80)2 + (2 × 80 × 2) + (2)2] – [(20)2 – (2 × 20 × 2) + (2)2]

= (6400 + 320 + 4) – (400 – 80 + 4)

= 6724 – 324 = 6400

Ans: (c)

(16) (197 × 203)

= (200 – 3) × (200 + 3)

= (200)2 – (3)2

= 40000 – 9 = 39991

Ans: (a)

(17) If (a + b) = 12 and ab = 14, then (a2 + b2) =?

⇒ (a + b) = 12

⇒ (a + b)2 = (12)2

⇒ a2 + 2ab + b2 = 144

⇒ (a2 + b2) + (2 × 14) = 144

⇒ (a2 + b2) = 144 – 28 = 116

Ans: (b)

(18) If (a – b) = 7 and ab = 9, then, (a2 + b2) =?

⇒ (a – b) = 7

⇒ (a – b)2 = 72

⇒ a2 – 2ab + b2 = 49

⇒ (a2 + b2) – (2 × 9) = 49

⇒ (a2 + b2) = 49 + 18

⇒ (a2 + b2) = 67

Ans: (a)

(19) If x = 10, then the value of (4x2 + 20x + 25) =?

= 4x2 + 20x + 25

= [4 × (10)2] + (20 × 10) + 25

= (4 × 100) + 200 + 25

= 400 + 200 + 25

= 625

Ans: (c)

Updated: May 30, 2022 — 2:11 pm

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