Question

Which of the following is a factor of
$(x+y{)}^3-(x^3+y^3)$?

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

Answer 1

The correct option is C

$3xy$

$\text{Let}P\left(x\right)=(x+y)(x+y{)}^2-(x+y\left)\right(x^2-xy+y^2)$

$=(x+y)(x^2+2xy+y^2)-(x+y)(x^2-xy+y^2)$

$=(x+y)(x^2+2xy+y^2-x^2+xy-y^2)$

[Taking $(x+y)$ as common]

$=(x+y)\left(3xy\right)$

Hence, from the given options 3xy is a factor of the given polynomial.