Algebra Examples

$100 m^{2} n^{4} - \frac{1}{16} x^{8}$

Step 1

Rewrite $100 m^{2} n^{4}$ as ${(10 m n^{2})}^{2}$ .

${(10 m n^{2})}^{2} - \frac{1}{16} x^{8}$

Step 2

Rewrite $\frac{1}{16} x^{8}$ as ${(\frac{1}{4} x^{4})}^{2}$ .

${(10 m n^{2})}^{2} - {(\frac{1}{4} x^{4})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 10 m n^{2}$ and $b = \frac{1}{4} x^{4}$ .

$(10 m n^{2} + \frac{1}{4} x^{4}) (10 m n^{2} - (\frac{1}{4} x^{4}))$

Step 4

Simplify.

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Step 4.1

Combine $\frac{1}{4}$ and $x^{4}$ .

$(10 m n^{2} + \frac{x^{4}}{4}) (10 m n^{2} - (\frac{1}{4} x^{4}))$

Step 4.2

Combine $\frac{1}{4}$ and $x^{4}$ .

$(10 m n^{2} + \frac{x^{4}}{4}) (10 m n^{2} - \frac{x^{4}}{4})$