Algebra Examples

$x^{2} y^{4} - b^{2} c^{4}$

Step 1

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

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

Step 2

Rewrite $b^{2} c^{4}$ as ${(b c^{2})}^{2}$ .

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

Step 3

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

$(x y^{2} + b c^{2}) (x y^{2} - (b c^{2}))$

Step 4

Remove parentheses.

$(x y^{2} + b c^{2}) (x y^{2} - b c^{2})$