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Question 17
Which of the following is a factor of (x+y)3(x3+y3)?

A) x2+y2+2xy
B) x2+y2xy
C) xy2
​​​​​​​D) 3xy

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Solution

The answer is D.
Now, (x+y)3(x3+y3)=(x+y)3(x+y)(x2xy+y2)
[Using identity, a3+b3=(a+b)(a2ab+b2)]
=(x+y)[(x+y)2(x2xy+y2)]
=(x+y)(x2+y2+2xyx2+xyy2)
[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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