Precalculus Examples

$2 {(3 x - 7)}^{2} + x (3 x - 7)$

Step 1

Factor $3 x - 7$ out of $2 {(3 x - 7)}^{2} + x (3 x - 7)$ .

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Step 1.1

Factor $3 x - 7$ out of $2 {(3 x - 7)}^{2}$ .

$(3 x - 7) (2 (3 x - 7)) + x (3 x - 7)$

Step 1.2

Factor $3 x - 7$ out of $x (3 x - 7)$ .

$(3 x - 7) (2 (3 x - 7)) + (3 x - 7) x$

Step 1.3

Factor $3 x - 7$ out of $(3 x - 7) (2 (3 x - 7)) + (3 x - 7) x$ .

$(3 x - 7) (2 (3 x - 7) + x)$

Step 2

Apply the distributive property.

$(3 x - 7) (2 (3 x) + 2 \cdot - 7 + x)$

Step 3

Multiply $3$ by $2$ .

$(3 x - 7) (6 x + 2 \cdot - 7 + x)$

Step 4

Multiply $2$ by $- 7$ .

$(3 x - 7) (6 x - 14 + x)$

Step 5

Add $6 x$ and $x$ .

$(3 x - 7) (7 x - 14)$

Step 6

Factor.

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Step 6.1

Factor $7$ out of $7 x - 14$ .

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Step 6.1.1

Factor $7$ out of $7 x$ .

$(3 x - 7) (7 (x) - 14)$

Step 6.1.2

Factor $7$ out of $- 14$ .

$(3 x - 7) (7 x + 7 \cdot - 2)$

Step 6.1.3

Factor $7$ out of $7 x + 7 \cdot - 2$ .

$(3 x - 7) (7 (x - 2))$

Step 6.2

Remove unnecessary parentheses.

$(3 x - 7) \cdot 7 (x - 2)$