Precalculus Examples

$5 x^{4} {(5 x - 6)}^{2} + x^{5} (2) (5 x - 6) (5)$

Step 1

Multiply $x^{5}$ by $2$ .

$5 x^{4} {(5 x - 6)}^{2} + x^{5} \cdot 2 (5 x - 6) \cdot 5$

Step 2

Factor $x^{4} (5 x - 6)$ out of $5 x^{4} {(5 x - 6)}^{2} + x^{5} \cdot 2 (5 x - 6) \cdot 5$ .

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Step 2.1

Factor $x^{4} (5 x - 6)$ out of $5 x^{4} {(5 x - 6)}^{2}$ .

$x^{4} (5 x - 6) (5 (5 x - 6)) + x^{5} \cdot 2 (5 x - 6) \cdot 5$

Step 2.2

Factor $x^{4} (5 x - 6)$ out of $x^{5} \cdot 2 (5 x - 6) \cdot 5$ .

$x^{4} (5 x - 6) (5 (5 x - 6)) + x^{4} (5 x - 6) ((x \cdot 2) \cdot 5)$

Step 2.3

Factor $x^{4} (5 x - 6)$ out of $x^{4} (5 x - 6) (5 (5 x - 6)) + x^{4} (5 x - 6) ((x \cdot 2) \cdot 5)$ .

$x^{4} (5 x - 6) (5 (5 x - 6) + (x \cdot 2) \cdot 5)$

Step 3

Multiply $5$ by $2$ .

$x^{4} (5 x - 6) (5 (5 x - 6) + x \cdot 10)$

Step 4

Factor $5$ out of $5 (5 x - 6) + x \cdot 10$ .

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Step 4.1

Factor $5$ out of $x \cdot 10$ .

$x^{4} (5 x - 6) (5 (5 x - 6) + 5 (x \cdot 2))$

Step 4.2

Factor $5$ out of $5 (5 x - 6) + 5 (x \cdot 2)$ .

$x^{4} (5 x - 6) (5 (5 x - 6 + x \cdot 2))$

Step 5

Move $2$ to the left of $x$ .

$x^{4} (5 x - 6) (5 (5 x - 6 + 2 x))$

Step 6

Factor.

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Step 6.1

Add $5 x$ and $2 x$ .

$x^{4} (5 x - 6) (5 (7 x - 6))$

Step 6.2

Remove unnecessary parentheses.

$x^{4} (5 x - 6) \cdot 5 (7 x - 6)$