Question

Factorise the following
1) 1 - 64a³ - 12a + 48a²
2) 8p³ + 12/5p² + 6/25p + 1/125​

[ With explanation ]​

Answer 1

Step-by-step explanation:

1) 1 - 64a³ - 12a + 48a²

=(1)3−(4a)3−3(1)2(4a)+3(1)(4a)2

Suitable identities is x3−y3−3x2y+3xy2=(x−y)3

= (1)3−(4a)3−3(1)2(4a)+3(1)(4a)2=(1−4a)3

2) 8p³ + 12/5p² + 6/25p + 1/125

= (2p)3 + (15)3 + 3(2p)2(15) + 3(2p) (15)2

= (2p + 15)3

[∵ a3 + b3 + 3a2b + 3ab2 = (a + b) 3]

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