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