Algebra Examples

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

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 $b = b + c$ .

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

Step 2

Simplify.

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Step 2.1

Add $b$ and $b$ .

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Subtract $b$ from $b$ .

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

Step 2.4

Add $a$ and $0$ .

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