Pre-Algebra Examples

$x^{2} - {(y - 1)}^{2}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y - 1$ .

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

Step 2

Simplify.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- 1$ by $- 1$ .

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