Basic Math Examples

$81 a^{2} - b^{2} c^{2}$

Step 1

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

${(9 a)}^{2} - b^{2} c^{2}$

Step 2

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

${(9 a)}^{2} - {(b c)}^{2}$

Step 3

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

$(9 a + b c) (9 a - (b c))$

Step 4

Remove parentheses.

$(9 a + b c) (9 a - b c)$