Mathematics
Factorise :
a3 - 27b3 + 2a2b - 6ab2
Factorisation
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Answer
Given,
a3 - 27b3 + 2a2b - 6ab2
= (a)3 - (3b)3 + 2ab(a - 3b)
= (a - 3b)[(a)2 + a × 3b + (3b)2] + 2ab(a - 3b)
= (a - 3b)[a2 + 3ab + 9b2] + 2ab(a - 3b)
= (a - 3b)(a2 + 3ab + 9b2 + 2ab)
= (a - 3b)(a2 + 5ab + 9b2).
Hence, a3 - 27b3 + 2a2b - 6ab2 = (a - 3b)(a2 + 5ab + 9b2).
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