Algebra Examples

$x^{2} - 24 x + 144 - y^{2}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $144$ as $12^{2}$ .

$x^{2} - 24 x + 12^{2} - y^{2}$

Step 1.2

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

$24 x = 2 \cdot x \cdot 12$

Step 1.3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 12 + 12^{2} - y^{2}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 12$ .

${(x - 12)}^{2} - y^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x - 12$ and $b = y$ .

$(x - 12 + y) (x - 12 - y)$