Algebra Examples

${(a - b)}^{2} - {(c - d)}^{2}$

Step 1

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

$(a - b + c - d) (a - b - (c - d))$

Step 2

Simplify.

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Step 2.1

Apply the distributive property.

$(a - b + c - d) (a - b - c - - d)$

Step 2.2

Multiply $- - d$ .

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

$(a - b + c - d) (a - b - c + 1 d)$

Step 2.2.2

Multiply $d$ by $1$ .

$(a - b + c - d) (a - b - c + d)$