Algebra Examples

$x^{4} - 100 y^{2}$

Step 1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

${(x^{2})}^{2} - 100 y^{2}$

Step 2

Rewrite $100 y^{2}$ as ${(10 y)}^{2}$ .

${(x^{2})}^{2} - {(10 y)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 10 y$ .

$(x^{2} + 10 y) (x^{2} - (10 y))$

Step 4

Multiply $10$ by $- 1$ .

$(x^{2} + 10 y) (x^{2} - 10 y)$