Algebra Examples

$4 a^{2} b^{2} - 25 m^{2} n^{2}$

Step 1

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

${(2 a b)}^{2} - 25 m^{2} n^{2}$

Step 2

Rewrite $25 m^{2} n^{2}$ as ${(5 m n)}^{2}$ .

${(2 a b)}^{2} - {(5 m n)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 a b$ and $b = 5 m n$ .

$(2 a b + 5 m n) (2 a b - (5 m n))$

Step 4

Simplify.

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Step 4.1

Multiply $5$ by $- 1$ .

$(2 a b + 5 m n) (2 a b - 5 (m n))$

Step 4.2

Remove parentheses.

$(2 a b + 5 m n) (2 a b - 5 m n)$