Algebra Examples

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

Step 1

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

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Step 1.1

Factor $5 x - 7$ out of $7 {(5 x - 7)}^{2}$ .

$(5 x - 7) (7 (5 x - 7)) + 9 (5 x - 7) (x + 9)$

Step 1.2

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

$(5 x - 7) (7 (5 x - 7)) + (5 x - 7) (9 (x + 9))$

Step 1.3

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

$(5 x - 7) (7 (5 x - 7) + 9 (x + 9))$

Step 2

Apply the distributive property.

$(5 x - 7) (7 (5 x) + 7 \cdot - 7 + 9 (x + 9))$

Step 3

Multiply $5$ by $7$ .

$(5 x - 7) (35 x + 7 \cdot - 7 + 9 (x + 9))$

Step 4

Multiply $7$ by $- 7$ .

$(5 x - 7) (35 x - 49 + 9 (x + 9))$

Step 5

Apply the distributive property.

$(5 x - 7) (35 x - 49 + 9 x + 9 \cdot 9)$

Step 6

Multiply $9$ by $9$ .

$(5 x - 7) (35 x - 49 + 9 x + 81)$

Step 7

Add $35 x$ and $9 x$ .

$(5 x - 7) (44 x - 49 + 81)$

Step 8

Add $- 49$ and $81$ .

$(5 x - 7) (44 x + 32)$

Step 9

Factor.

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Step 9.1

Factor $4$ out of $44 x + 32$ .

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Step 9.1.1

Factor $4$ out of $44 x$ .

$(5 x - 7) (4 (11 x) + 32)$

Step 9.1.2

Factor $4$ out of $32$ .

$(5 x - 7) (4 (11 x) + 4 (8))$

Step 9.1.3

Factor $4$ out of $4 (11 x) + 4 (8)$ .

$(5 x - 7) (4 (11 x + 8))$

Step 9.2

Remove unnecessary parentheses.

$(5 x - 7) \cdot 4 (11 x + 8)$