Algebra Examples

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

Step 1

Rewrite $4$ as $2^{2}$ .

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

Step 2

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

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

Step 3

Apply the distributive property.

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

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $2 - x - y$ .

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Step 4.1.1

Move $2$ .

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

Step 4.1.2

Factor $- 1$ out of $- x$ .

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

Step 4.1.3

Factor $- 1$ out of $- y$ .

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

Step 4.1.4

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 4.1.5

Factor $- 1$ out of $- (x) - (y)$ .

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

Step 4.1.6

Factor $- 1$ out of $- (x + y) - 1 (- 2)$ .

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

Step 4.2

Remove unnecessary parentheses.

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

Step 5

Factor out negative.

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

Step 6

Remove unnecessary parentheses.

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