Algebra Examples

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

Step 1

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

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

Step 2

Simplify.

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Step 2.1

Add $x$ and $x$ .

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

Step 2.2

Subtract $y$ from $y$ .

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

Step 2.3

Add $2 x$ and $0$ .

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

Step 2.4

Apply the distributive property.

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

Step 2.5

Multiply $- - y$ .

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Step 2.5.1

Multiply $- 1$ by $- 1$ .

$2 x (x + y - x + 1 y)$

Step 2.5.2

Multiply $y$ by $1$ .

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

Step 2.6

Subtract $x$ from $x$ .

$2 x (y + 0 + y)$

Step 2.7

Add $y$ and $0$ .

$2 x (y + y)$

Step 2.8

Factor.

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Step 2.8.1

Add $y$ and $y$ .

$2 x (2 y)$

Step 2.8.2

Remove unnecessary parentheses.

$2 x \cdot 2 y$

Step 2.9

Multiply $2$ by $2$ .

$4 x y$