Precalculus 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

Subtract $b$ from $b$ .

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

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

Multiply $- - b$ .

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Step 2.5.1

Multiply $- 1$ by $- 1$ .

$2 a (a + b - a + 1 b)$

Step 2.5.2

Multiply $b$ by $1$ .

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

Step 2.6

Subtract $a$ from $a$ .

$2 a (b + 0 + b)$

Step 2.7

Add $b$ and $0$ .

$2 a (b + b)$

Step 2.8

Factor.

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Step 2.8.1

Add $b$ and $b$ .

$2 a (2 b)$

Step 2.8.2

Remove unnecessary parentheses.

$2 a \cdot 2 b$

Step 2.9

Multiply $2$ by $2$ .

$4 a b$