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Question
Factorise:
a3 - 27b3 + 2a2b - 6ab2
Sum
Solution
a3 - 27b3 + 2a2b - 6ab2
We know that,
a3 - b3 = (a - b)(a2 + ab + b2) ...(1)
a3 - 27b3 + 2a2b - 6ab2
= (a)3 - (3b)3 + 2ab(a - 3b)
= (a - 3b)[a2 + a × 3b + (3b)2] + 2ab(a - 3b) ...[From(1)]
= (a - 3b)[a2 + 3ab + 9b2] + 2ab(a - 3b)
= (a - 3b)[a2 + 3ab + 9b2 + 2ab]
= (a - 3b)[a2 + 5ab + 9b2]
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Method of Factorisation : the Sum Or Difference of Two Cubes
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