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which of the following is a factor o...

which of the following is a factor of `(x+y)^(3)-(x^(3)+y^(3))`?

A

`x^(2)+y^(2)+2xy`

B

`x^(2)+y^(2)-xy`

C

`xy^(2)`

D

`3xy`

Text Solution

Verified by Experts

The correct Answer is:
D
Now ,`(x+y)^(3)=(x^(3)+y^(3))=(x+y)^(3)-(x+y)(x^(2)-xy+y^(2))`
`" " ["using identity ," a^(3)+b^(3)=(a+b)(a^(2)-ab+b^(2))]`
`=(x+y)[(x+y)^(2)-(x^(2)xy+y^(2))]`
`=(x+y)(x^(2)+y^(2)+2xy-y^(2))`
`" " ["using identity," (a+b)^(2)=a^(2)+b^(2)+2ab)]`
`=(x+y(3xy)`
Hence , one of the factor of given polynomial is 3xy.
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