Algebra Examples

$16 m^{6} - n^{6}$

Step 1

Rewrite $16 m^{6}$ as ${(4 m^{3})}^{2}$ .

${(4 m^{3})}^{2} - n^{6}$

Step 2

Rewrite $n^{6}$ as ${(n^{3})}^{2}$ .

${(4 m^{3})}^{2} - {(n^{3})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 m^{3}$ and $b = n^{3}$ .

$(4 m^{3} + n^{3}) (4 m^{3} - n^{3})$