Factorise the following:
8x3 + y3
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8x3 + y3 = (2x)3 + (y)3
We know that,
a3 + b3 = (a + b)(a2 - ab + b2)
∴ (2x)3 + (y)3 = (2x + y)[(2x)2 - 2xy + (y)2]
= (2x + y)(4x2 - 2xy + y2).
Hence, 8x3 + y3 = (2x + y)(4x2 - 2xy + y2).
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4(2a - 3)2 - 3(2a - 3)(a - 1) - 7(a - 1)2
(2x2 + 5x)(2x2 + 5x - 19) + 84
64x3 - 125y3
64x3 + 1