Precalculus Examples

$- 36 k^{2} + 49$

Step 1

Factor $- 1$ out of $- 36 k^{2} + 49$ .

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Step 1.1

Factor $- 1$ out of $- 36 k^{2}$ .

$- (36 k^{2}) + 49$

Step 1.2

Rewrite $49$ as $- 1 (- 49)$ .

$- (36 k^{2}) - 1 (- 49)$

Step 1.3

Factor $- 1$ out of $- (36 k^{2}) - 1 (- 49)$ .

$- (36 k^{2} - 49)$

Step 2

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

$- ({(6 k)}^{2} - 49)$

Step 3

Rewrite $49$ as $7^{2}$ .

$- ({(6 k)}^{2} - 7^{2})$

Step 4

Factor.

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Step 4.1

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

$- ((6 k + 7) (6 k - 7))$

Step 4.2

Remove unnecessary parentheses.

$- (6 k + 7) (6 k - 7)$