Mathematics
Factorise the following:
27x3y3 - 8
Factorisation
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Answer
27x3y3 - 8 = (3xy)3 - (2)3.
We know that,
a3 - b3 = (a - b)(a2 + ab + b2)
(3xy)3 - (2)3 = (3xy - 2)[(3xy)2 + 3xy.2 + 22]
= (3xy - 2)(9x2y2 + 6xy + 4).
Hence, 27x3y3 - 8 = (3xy - 2)(9x2y2 + 6xy + 4).
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