Precalculus Examples

$9 {(5 x - 2)}^{2} - 7 (5 x - 2) (3 x + 4)$

Step 1

Factor $5 x - 2$ out of $9 {(5 x - 2)}^{2} - 7 (5 x - 2) (3 x + 4)$ .

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Step 1.1

Factor $5 x - 2$ out of $9 {(5 x - 2)}^{2}$ .

$(5 x - 2) (9 (5 x - 2)) - 7 (5 x - 2) (3 x + 4)$

Step 1.2

Factor $5 x - 2$ out of $- 7 (5 x - 2) (3 x + 4)$ .

$(5 x - 2) (9 (5 x - 2)) + (5 x - 2) (- 7 (3 x + 4))$

Step 1.3

Factor $5 x - 2$ out of $(5 x - 2) (9 (5 x - 2)) + (5 x - 2) (- 7 (3 x + 4))$ .

$(5 x - 2) (9 (5 x - 2) - 7 (3 x + 4))$

Step 2

Apply the distributive property.

$(5 x - 2) (9 (5 x) + 9 \cdot - 2 - 7 (3 x + 4))$

Step 3

Multiply $5$ by $9$ .

$(5 x - 2) (45 x + 9 \cdot - 2 - 7 (3 x + 4))$

Step 4

Multiply $9$ by $- 2$ .

$(5 x - 2) (45 x - 18 - 7 (3 x + 4))$

Step 5

Apply the distributive property.

$(5 x - 2) (45 x - 18 - 7 (3 x) - 7 \cdot 4)$

Step 6

Multiply $3$ by $- 7$ .

$(5 x - 2) (45 x - 18 - 21 x - 7 \cdot 4)$

Step 7

Multiply $- 7$ by $4$ .

$(5 x - 2) (45 x - 18 - 21 x - 28)$

Step 8

Subtract $21 x$ from $45 x$ .

$(5 x - 2) (24 x - 18 - 28)$

Step 9

Subtract $28$ from $- 18$ .

$(5 x - 2) (24 x - 46)$

Step 10

Factor.

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Step 10.1

Factor $2$ out of $24 x - 46$ .

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Step 10.1.1

Factor $2$ out of $24 x$ .

$(5 x - 2) (2 (12 x) - 46)$

Step 10.1.2

Factor $2$ out of $- 46$ .

$(5 x - 2) (2 (12 x) + 2 (- 23))$

Step 10.1.3

Factor $2$ out of $2 (12 x) + 2 (- 23)$ .

$(5 x - 2) (2 (12 x - 23))$

Step 10.2

Remove unnecessary parentheses.

$(5 x - 2) \cdot 2 (12 x - 23)$