Question:
Which of the following is a factor of (x+ y)3 – (x3 + y3)?
(a) x2 + y2 + 2 xy
(b) x2 + y2 – xy
(c) xy2
(d) 3xy
Solution:
(d) 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 + 2 ab)]
= (x + y) (3xy)
Hence, one of the factor of given polynomial is 3xy.
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