Question
Which of the following is a factor of
(x+y)3−(x3+y3)?
(x+y)3−(x3+y3)?
Answer: Option C
:
C
LetP(x)=(x+y)(x+y)2−(x+y)(x2−xy+y2)
=(x+y)(x2+2xy+y2)−(x+y)(x2−xy+y2)
=(x+y)(x2+2xy+y2−x2+xy−y2)
[Taking (x+y) as common]
=(x+y)(3xy)
Hence, from the given options3xy is a factor ofthe given polynomial.
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:
C
LetP(x)=(x+y)(x+y)2−(x+y)(x2−xy+y2)
=(x+y)(x2+2xy+y2)−(x+y)(x2−xy+y2)
=(x+y)(x2+2xy+y2−x2+xy−y2)
[Taking (x+y) as common]
=(x+y)(3xy)
Hence, from the given options3xy is a factor ofthe given polynomial.
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