Algebra Examples

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

Step 1

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

$(a + x + x + 2) (a + x - (x + 2))$

Step 2

Simplify.

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Step 2.1

Add $x$ and $x$ .

$(a + 2 x + 2) (a + x - (x + 2))$

Step 2.2

Apply the distributive property.

$(a + 2 x + 2) (a + x - x - 1 \cdot 2)$

Step 2.3

Multiply $- 1$ by $2$ .

$(a + 2 x + 2) (a + x - x - 2)$

Step 2.4

Subtract $x$ from $x$ .

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

Step 2.5

Add $a$ and $0$ .

$(a + 2 x + 2) (a - 2)$