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