Precalculus Examples

$4 x^{2} - {(x + y)}^{2}$

Step 1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Step 2

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

$(2 x + x + y) (2 x - (x + y))$

Step 3

Simplify.

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Step 3.1

Add $2 x$ and $x$ .

$(3 x + y) (2 x - (x + y))$

Step 3.2

Apply the distributive property.

$(3 x + y) (2 x - x - y)$

Step 3.3

Subtract $x$ from $2 x$ .

$(3 x + y) (x - y)$