Factor m^2-x^2-y^2+2xy

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

Step 1

Regroup terms.

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

Step 2

Factor $- 1$ out of $- x^{2} - y^{2} + 2 x y$ .

Move $- y^{2}$ .

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

Factor $- 1$ out of $- x^{2}$ .

$m^{2} - (x^{2}) + 2 x y - y^{2}$

Factor $- 1$ out of $2 x y$ .

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

Factor $- 1$ out of $- y^{2}$ .

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

Factor $- 1$ out of $- (x^{2}) - (- 2 x y)$ .

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

Factor $- 1$ out of $- (x^{2} - 2 x y) - (y^{2})$ .

$m^{2} - (x^{2} - 2 x y + y^{2})$

Step 3

Factor using the perfect square rule.

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 x y = 2 \cdot x \cdot y$

Rewrite the polynomial.

$m^{2} - (x^{2} - 2 \cdot x \cdot y + y^{2})$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = y$ .

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = x - y$ .

$(m + x - y) (m - (x - y))$

Step 5

Simplify.

Apply the distributive property.

$(m + x - y) (m - x - - y)$

Multiply $- - y$ .

Multiply $- 1$ by $- 1$ .

$(m + x - y) (m - x + 1 y)$

Multiply $y$ by $1$ .

$(m + x - y) (m - x + y)$

Factor m^2-x^2-y^2+2xy

Related Questions

Support LCMGCF.com by disabling your adblocker.