Algebra Examples

$49 + 76 n^{2} + 64 n^{4}$

Step 1

Rewrite the middle term.

$49 + 2 \cdot 7 (8 n^{2}) - 36 n^{2} + 64 n^{4}$

Step 2

Rearrange terms.

$49 + 2 \cdot 7 (8 n^{2}) + 64 n^{4} - 36 n^{2}$

Step 3

Factor first three terms by perfect square rule.

${(7 + 8 n^{2})}^{2} - 36 n^{2}$

Step 4

Rewrite $36 n^{2}$ as ${(6 n)}^{2}$ .

${(7 + 8 n^{2})}^{2} - {(6 n)}^{2}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 + 8 n^{2}$ and $b = 6 n$ .

$(7 + 8 n^{2} + 6 n) (7 + 8 n^{2} - (6 n))$

Step 6

Simplify.

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Step 6.1

Reorder terms.

$(8 n^{2} + 6 n + 7) (7 + 8 n^{2} - (6 n))$

Step 6.2

Multiply $6$ by $- 1$ .

$(8 n^{2} + 6 n + 7) (7 + 8 n^{2} - 6 n)$

Step 6.3

Reorder terms.

$(8 n^{2} + 6 n + 7) (8 n^{2} - 6 n + 7)$