Factor 16-(x+y)^2

$16 - {(x + y)}^{2}$

Step 1

Rewrite $16$ as $4^{2}$ .

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = x + y$ .

$(4 + x + y) (4 - (x + y))$

Step 3

Apply the distributive property.

$(4 + x + y) (4 - x - y)$

Step 4

Factor.

Factor $- 1$ out of $4 - x - y$ .

Move $4$ .

$(4 + x + y) (- x - y + 4)$

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

$(4 + x + y) (- (x) - y + 4)$

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

$(4 + x + y) (- (x) - (y) + 4)$

Rewrite $4$ as $- 1 (- 4)$ .

$(4 + x + y) (- (x) - (y) - 1 (- 4))$

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

$(4 + x + y) (- (x + y) - 1 (- 4))$

Factor $- 1$ out of $- (x + y) - 1 (- 4)$ .

$(4 + x + y) (- (x + y - 4))$

Remove unnecessary parentheses.

$(4 + x + y) \cdot - 1 (x + y - 4)$

Step 5

Factor out negative.

$- ((4 + x + y) (x + y - 4))$

Step 6

Remove unnecessary parentheses.

$- (4 + x + y) (x + y - 4)$

Factor 16-(x+y)^2

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