Factor (x-y)^2-(x-z)^2

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

Step 1

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

$(x - y + x - z) (x - y - (x - z))$

Step 2

Simplify.

Add $x$ and $x$ .

$(2 x - y - z) (x - y - (x - z))$

Apply the distributive property.

$(2 x - y - z) (x - y - x - - z)$

Multiply $- - z$ .

Multiply $- 1$ by $- 1$ .

$(2 x - y - z) (x - y - x + 1 z)$

Multiply $z$ by $1$ .

$(2 x - y - z) (x - y - x + z)$

Subtract $x$ from $x$ .

$(2 x - y - z) (- y + 0 + z)$

Add $- y$ and $0$ .

$(2 x - y - z) (- y + z)$

Step 3

Factor.

Factor $- 1$ out of $- y + z$ .

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

$(2 x - y - z) (- (y) + z)$

Factor $- 1$ out of $z$ .

$(2 x - y - z) (- (y) - 1 (- z))$

Factor $- 1$ out of $- (y) - 1 (- z)$ .

$(2 x - y - z) (- (y - z))$

Remove unnecessary parentheses.

$(2 x - y - z) \cdot - 1 (y - z)$

Step 4

Factor out negative.

$- ((2 x - y - z) (y - z))$

Step 5

Remove unnecessary parentheses.

$- (2 x - y - z) (y - z)$

Factor (x-y)^2-(x-z)^2

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