Mathematics
Factorise:
a2 - 4b2 + a3 - 8b3 - (a - 2b)2
Factorisation
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Answer
Given,
⇒ a2 - 4b2 + a3 - 8b3 - (a - 2b)2
⇒ (a)2 - (2b)2 + (a)3 - (2b)3 - (a - 2b)(a - 2b)
By using the identity,
(a2 - b2) = (a + b)(a - b) and (a3 - b3) = (a - b)(a2 + ab + b2)
⇒ (a + 2b)(a - 2b) + (a - 2b)(a2 + a × 2b + (2b)2) - (a - 2b)(a - 2b)
⇒ (a - 2b)[(a + 2b) + (a2 + 2ab + 4b2) - (a - 2b)]
⇒ (a - 2b)[a + 2b - a + 2b + (a2 + 2ab + 4b2)]
⇒ (a - 2b)(a2 + 2ab + 4b2 + 4b).
Hence, a2 - 4b2 + a3 - 8b3 - (a - 2b)2 = (a - 2b)(a2 + 2ab + 4b2 + 4b).
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