# How do you solve xy(x-y)^2?I know how to solve polynomials, however this is not a special product formula, and I'm able to use FOIL. I feel like I'm missing something really easy here...  I...

How do you solve xy(x-y)^2?

I know how to solve polynomials, however this is not a special product formula, and I'm able to use FOIL. I feel like I'm missing something really easy here...

I appreciate the help.

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to expand the square either using the special product `(a - b)^2 = a^2 - 2ab + b^2` , or performing the multiplication `(x-y)(x-y)`  using the property of distributivity over addition, such that:

`(x-y)(x-y) = x(x-y) - y(x-y)`

`(x-y)(x-y) = x^2 - xy - yx + y^2 => (x-y)(x-y) = x^2 - 2xy + y^2`

You need to continue to perform the multiplication, such that:

`xy(x-y)^2 = xy(x^2 - 2xy + y^2) => xy(x-y)^2 = x^3y - 2x^2y^2 + xy^3`

Hence, evaluating the given product, using the property of distributivity of multiplication over addition, yields `xy(x-y)^2 = x^3y - 2x^2y^2 + xy^3.`

arif7hs | Student, Undergraduate | (Level 1) eNoter

Posted on

Q.      xy(x-y)^2

ans: =xy ( x^2 - 2xy + y^2 ) [ we know that, (x-y)^2 = x^2 - 2xy +

y^2)]

= x^3.y - 2x^2.y^2 + x.y^3

shossinei | Student, Undergraduate | eNotes Newbie

Posted on

Alright I figured out the answer, so for the benefit of others I will answer it here!

xy(x-y)^2

So it actually is a special product formula, you must solve (x-y)^2 first.

x^2 -2(x)(y) + y^2 {Which becomes ->}

x^2 -2xy + y^2 {then you multipy this polynomial by xy}

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

x^3y -2x^2y^2 + xy^3

And that's the answer! Note: the up arrows and the number directly after it mean that it is a square/cube. Ex. x^2=x squared.