Question

Co
8. Factorise each of the following:
(i) 8a + b3 +12a+b +6ab2
(ii) 27-125a - 135a + 225a2​

Answer 1

Answer:

(i)8a + b3 +12a+b +6ab2

=(2a-b)(4a²+2ab+b²)-6ab(2a-b)

=(2a-b)(4a²+2ab+b²-6ab)

=(2a-b)(4a²-4ab+b²)

=(2a-b){(2a)²-2×2a×b+(b)²}

=(2a-b)(2a-b)²

=(2a-b)(2a-b)(2a-b)

ii) 27 – 125a³ – 135a + 225a²

SOL: 27 – 125a³– 135a + 225a²

= (3)³ – (5a)³ – 135a + 225a²

= (3)³ – (5a)³ – 45a(3 – 5a)

= (3)³ – (5a)³ – 3(3)(5a)(3 – 5a)

Again Using (x – y)³ = x³ – y³ – 3xy (x – y)

Putting nd we get x = 3, y = 5a

= (3 – 5a)³

= (3 – 5a) (3 – 5a) (3 – 5a)