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Question
Which of the following is a factor of (x + y)3 – (x3 + y3)?
Options
x2 + y2 + 2xy
x2 + y2 – xy
xy2
3xy
Solution
3xy
Explanation:
Now, (x + y)3 – (x3 + y3) = (x + y) – (x + y)(x2 – xy + y2) ...[Using identity, a3 + b3 = (a + b)(a2 – ab + b2)]
= (x + y)[(x + y)2 – (x2 – xy + y2)]
= (x + y)(x2 + y2 + 2xy – x2 + xy – y2) ...[Using identity, (a + b)2 = a2 + b2 + 2ab)]
= (x + y)(3xy)
Hence, one of the factor of given polynomial is 3xy.
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