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Question
Simplify:
(x + y)3 − (x − y)3
Simplify
Solution
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
(x + y)3 − (x − y)3
(x + y)3 − (x − y)3 = {(x + y) − (x − y)}{(x + y)2 + (x + y)(x − y) + (x − y)2}
= 2y(x2 + 2xy + y2 + x2 − y2 + x2 − 2xy + y2)
= 2y (3x2 + y2)
= 2y × 3x2 + 2y × y2
= 6x2y + 2y3
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