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

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

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Answer 1 · 2016-04-12T15:49:12

The factors are

$(x - y) (x - y)$ $(x-y)(x-y)$
or
${(x - y)}^{2}$ $(x-y)^2$

Explanation:

We need to factor the trinomial
$x^{2} - 2 x y + y^{2}$ $x^2-2xy+y^2$

The factors of $x^{2} = (x) (x)$ $x^2 = (x)(x)$
The factors of $y^{2} = (y) (y)$ $y^2 = (y)(y)$

Since the second sign is positive we are adding the factors meaning the signs of the factors need to be the same. Since the first sign is negative both signs must be negative.

The factors are

$(x - y) (x - y)$ $(x-y)(x-y)$
or
${(x - y)}^{2}$ $(x-y)^2$

Check by FOIL
Firsts $(x) (x) = x^{2}$ $(x)(x) = x^2$
Outers $(x) (- y) = - x y$ $(x)(-y) = -xy$
Inners $(- y) (x) = - x y$ $(-y)(x) = -xy$
Lasts $(- y) (- y) = y^{2}$ $(-y)(-y) = y^2$
combine the middle terms
$(- x y) + (- x y) = - 2 x y$ $(-xy)+(-xy) = -2xy$

$x^{2} - 2 x y + y^{2}$ $x^2-2xy+y^2$

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

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