Algebra Examples

$64 m^{2} - {(m - 2 n)}^{2}$

Step 1

Rewrite $64 m^{2}$ as ${(8 m)}^{2}$ .

${(8 m)}^{2} - {(m - 2 n)}^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 8 m$ and $b = m - 2 n$ .

$(8 m + m - 2 n) (8 m - (m - 2 n))$

Step 3

Simplify.

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Step 3.1

Add $8 m$ and $m$ .

$(9 m - 2 n) (8 m - (m - 2 n))$

Step 3.2

Apply the distributive property.

$(9 m - 2 n) (8 m - m - (- 2 n))$

Step 3.3

Multiply $- 2$ by $- 1$ .

$(9 m - 2 n) (8 m - m + 2 n)$

Step 3.4

Subtract $m$ from $8 m$ .

$(9 m - 2 n) (7 m + 2 n)$