vomi2xn

2023-03-02

Which of the following is a factor of (x+y)^3−(x^3+y^3)?
x^2−2xy+y^2
xy^2
3xy
x^2+xy+y^2

Macas6tl

$P\left(x\right)=\left(x+y\right)\left(x+y{\right)}^{2}-\left(x+y\right)\left({x}^{2}-xy+{y}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(x+y\right)\left({x}^{2}+2xy+{y}^{2}\right)-\left(x+y\right)\left({x}^{2}-xy+{y}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(x+y\right)\left({x}^{2}+2xy+{y}^{2}-{x}^{2}+xy-{y}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(x+y\right)\left(3xy\right)$