Algebra Examples

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

Step 1

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

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

Step 2

Simplify.

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Step 2.1

Add $y$ and $y$ .

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

Step 2.2

Factor $2$ out of $2 x + 2 y$ .

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Step 2.2.1

Factor $2$ out of $2 x$ .

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

Step 2.2.2

Factor $2$ out of $2 y$ .

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

Step 2.2.3

Factor $2$ out of $2 (x) + 2 (y)$ .

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

Step 2.3

Subtract $y$ from $y$ .

$2 (x + y) (2 x + 0)$

Step 2.4

Factor.

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Step 2.4.1

Add $2 x$ and $0$ .

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

Step 2.4.2

Remove unnecessary parentheses.

$2 (x + y) \cdot 2 x$

Step 2.5

Multiply $2$ by $2$ .

$4 (x + y) x$