Factor x^2-6x+9-y^2

$x^{2} - 6 x + 9 - y^{2}$

Step 1

Factor using the perfect square rule.

Rewrite $9$ as $3^{2}$ .

$x^{2} - 6 x + 3^{2} - y^{2}$

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

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 3 + 3^{2} - y^{2}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 3$ .

${(x - 3)}^{2} - y^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x - 3$ and $b = y$ .

$(x - 3 + y) (x - 3 - y)$

Factor x^2-6x+9-y^2

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