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Question
Simplify.
(2a + b)3 − (2a − b)3
Simplify
Solution
We know that,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a − b)3 = a3 − 3a2b + 3ab2 − b3
(2a + b)3 − (2a − b)3
= [(2a)3 + 3(2a)2(b) + 3(2a)(b)2 + (b)3] − [(2a)3 − 3(2a)2(b) + 3(2a)(b)2 − (b)3]
= 8a3 + 3(4a2)(b) + 3(2a)(b2) + b3 − 8a3 + 3(4a2)(b) − 3(2a)(b2) + b3
= 8a3 − 8a3 + 12a2b + 12a2b + 6ab2 − 6ab2 + b3 + b3
= 12a2b + b3 + 12a2b + b3
= 24a2b + 2b3
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