Factorise the following:
64x3 - 125y3
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64x3 - 125y3 = (4x)3 - (5y)3.
We know that,
a3 - b3 = (a - b)(a2 + ab + b2)
∴ (4x)3 - (5y)3 = (4x - 5y)[(4x)2 + 4x(5y) + (5y)2]
= (4x - 5y)(16x2 + 20xy + 25y2).
Hence, 64x3 - 125y3 = (4x - 5y)(16x2 + 20xy + 25y2).
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