Algebra Examples

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

Step 1

Factor using the perfect square rule.

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Step 1.1

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

$2 x y = 2 \cdot x \cdot y$

Step 1.2

Rewrite the polynomial.

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

Step 1.3

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

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

Step 2

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

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

Step 3

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

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