How do you factor $x^{3} y + 2 x^{2} y^{2} + x y^{3}$ $x^3y + 2x^2y^2 + xy^3$ ?

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Answer 1 · 2015-05-05T13:20:02

Extract the obvious common factor $(x y)$ $(xy)$

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

Recognize the second term as a square of sum
$= (x y) {(x + y)}^{2}$ $=(xy)(x+y)^2$

How do you factor x^3y + 2x^2y^2 + xy^3x3y+2x2y2+xy3x^3y + 2x^2y^2 + xy^3?