Basic Math Examples

$4 y^{4} - 81 b^{2}$

Step 1

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

${(2 y^{2})}^{2} - 81 b^{2}$

Step 2

Rewrite $81 b^{2}$ as ${(9 b)}^{2}$ .

${(2 y^{2})}^{2} - {(9 b)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 y^{2}$ and $b = 9 b$ .

$(2 y^{2} + 9 b) (2 y^{2} - (9 b))$

Step 4

Multiply $9$ by $- 1$ .

$(2 y^{2} + 9 b) (2 y^{2} - 9 b)$