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  • Which of the following is a factor of \left ( x+y \right )^{3}-\left ( x^{3}+y^{3} \right ) A. x^{2}+y^{2}+2xy\\ B. x^{2}+y^{2}-2xy\\ C. xy^{2}\\ D. 3xy

Which of the following is a factor of \left ( x+y \right )^{3}-\left ( x^{3}+y^{3} \right )

\\A. \ x^{2}+y^{2}+2xy\\ B. \ x^{2}+y^{2}-2xy\\ C. \ xy^{2}\\ D. \ 3xy

Answers (1)

(D) 3xy

Solution

Given,

\left ( x+y \right )^{3}-\left ( x^{3}+y^{3} \right ) 

We know that,

\left \{(a+b)^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{3} \right \}

So, (x+y)^{3}=x^{3}+y^{3}+3x^{2}y+3xy^{3}

\left ( x+y \right )^{3}-\left ( x^{3}+y^{3} \right )=x^{3}+y^{3}+3x^{2}y+3xy^{3}-x^{3}-y^{3}\\ =3x^{2}+3xy^{2}\\ =3xy(x+y)

The factors of the above polynomial are

3xy and (x+y)

Hence option D is correct

Posted by

infoexpert24

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