Basic Math Examples

${(a - b)}^{2} - {(a + b)}^{2}$

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 $b = a + b$ .

$(a - b + a + b) (a - b - (a + b))$

Step 2

Simplify.

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Step 2.1

Add $a$ and $a$ .

$(2 a - b + b) (a - b - (a + b))$

Step 2.2

Add $- b$ and $b$ .

$(2 a + 0) (a - b - (a + b))$

Step 2.3

Add $2 a$ and $0$ .

$2 a (a - b - (a + b))$

Step 2.4

Apply the distributive property.

$2 a (a - b - a - b)$

Step 2.5

Subtract $a$ from $a$ .

$2 a (- b + 0 - b)$

Step 2.6

Add $- b$ and $0$ .

$2 a (- b - b)$

Step 2.7

Factor.

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Step 2.7.1

Subtract $b$ from $- b$ .

$2 a (- 2 b)$

Step 2.7.2

Remove unnecessary parentheses.

$2 a \cdot - 2 b$

Step 2.8

Multiply $- 2$ by $2$ .

$- 4 a b$