## 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 + 7p ^{2} – 2r^{3} + 4) – (4p^{2} – 2q + 7r^{3} – 3) =?**

Ans: (d) (3p^{2} + 5q – 9r^{3} + 7)

Solution: 3q + 7p^{2} – 2r^{3} + 4 – 4p^{2} + 2q – 7r^{3} + 3

= 3p^{2} + 5q – 9r^{3} + 7

**(3) (x + 5) (x – 3) =?**

= x^{2} + 5x – 3x – 15

= x^{2} + 2x – 15

Ans: (d)

**(4) (2x+ 3) (3x – 1)**

= 6x^{2} + 9x – 2x – 3

= 6x^{2} + 7x – 3

Ans: (b)

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

= x^{2} + 4x + 4x + 16

= x^{2} + 8x + 16

Ans: (c)

**(6) (x – 6) (x – 6)**

= x^{2} – 6x – 6x + 36

= x^{2} – 12x + 36

Ans: (d)

**(7) (2x + 5) (2x – 5)**

= 4x^{2} + 10x – 10x – 25

= (4x^{2} – 25)

Ans: (b)

**(8) 8a ^{2}b^{3} ÷ (- 2ab)**

Ans: (c)

**(9) (2x ^{2} + 3x + 1) ÷ (x + 1)**

= 2x + 1

Ans: (b)

**(10) (x ^{2} – 4x + 4) ÷ (x – 2)**

= (x – 2)

Ans: (a)

**(11) (a + 1) (a – 1) (a ^{2} + 1)**

= [(a)^{2} – (1)^{2}] (a^{2} + 1)

= (a^{2} – 1) (a^{2} + 1)

= (a^{2})^{2} – (1)^{2}

= (a^{4} – 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 (a ^{2} + b^{2}) =?**

⇒ (a + b) = 12

⇒ (a + b)^{2} = (12)^{2}

⇒ a^{2} + 2ab + b^{2 }= 144

⇒ (a^{2} + b^{2}) + (2 × 14) = 144

⇒ (a^{2} + b^{2}) = 144 – 28 = 116

Ans: (b)

**(18) If (a – b) = 7 and ab = 9, then, (a ^{2} + b^{2}) =?**

⇒ (a – b) = 7

⇒ (a – b)^{2} = 7^{2}

⇒ a^{2} – 2ab + b^{2} = 49

⇒ (a^{2} + b^{2}) – (2 × 9) = 49

⇒ (a^{2} + b^{2}) = 49 + 18

⇒ (a^{2} + b^{2}) = 67

Ans: (a)

**(19) If x = 10, then the value of (4x ^{2} + 20x + 25) =?**

= 4x^{2} + 20x + 25

= [4 × (10)^{2}] + (20 × 10) + 25

= (4 × 100) + 200 + 25

= 400 + 200 + 25

= 625

Ans: (c)

Very very thanks to a website and helpful ex.

Thank You….