Factor y^2-x^2+8y+16

$y^{2} - x^{2} + 8 y + 16$

Step 1

Regroup terms.

$- x^{2} + y^{2} + 8 y + 16$

Step 2

Factor using the perfect square rule.

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

$- x^{2} + y^{2} + 8 y + 4^{2}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 y = 2 \cdot y \cdot 4$

Rewrite the polynomial.

$- x^{2} + y^{2} + 2 \cdot y \cdot 4 + 4^{2}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 4$ .

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

Step 3

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

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

Step 4

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

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

Factor y^2-x^2+8y+16

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