Algebra Examples

$5 {(3 - 4 x)}^{2} - 8 (3 - 4 x) (5 x - 1)$

Step 1

Factor $3 - 4 x$ out of $5 {(3 - 4 x)}^{2} - 8 (3 - 4 x) (5 x - 1)$ .

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Step 1.1

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

$(3 - 4 x) (5 (3 - 4 x)) - 8 (3 - 4 x) (5 x - 1)$

Step 1.2

Factor $3 - 4 x$ out of $- 8 (3 - 4 x) (5 x - 1)$ .

$(3 - 4 x) (5 (3 - 4 x)) + (3 - 4 x) (- 8 (5 x - 1))$

Step 1.3

Factor $3 - 4 x$ out of $(3 - 4 x) (5 (3 - 4 x)) + (3 - 4 x) (- 8 (5 x - 1))$ .

$(3 - 4 x) (5 (3 - 4 x) - 8 (5 x - 1))$

Step 2

Apply the distributive property.

$(3 - 4 x) (5 \cdot 3 + 5 (- 4 x) - 8 (5 x - 1))$

Step 3

Multiply $5$ by $3$ .

$(3 - 4 x) (15 + 5 (- 4 x) - 8 (5 x - 1))$

Step 4

Multiply $- 4$ by $5$ .

$(3 - 4 x) (15 - 20 x - 8 (5 x - 1))$

Step 5

Apply the distributive property.

$(3 - 4 x) (15 - 20 x - 8 (5 x) - 8 \cdot - 1)$

Step 6

Multiply $5$ by $- 8$ .

$(3 - 4 x) (15 - 20 x - 40 x - 8 \cdot - 1)$

Step 7

Multiply $- 8$ by $- 1$ .

$(3 - 4 x) (15 - 20 x - 40 x + 8)$

Step 8

Add $15$ and $8$ .

$(3 - 4 x) (- 20 x - 40 x + 23)$

Step 9

Subtract $40 x$ from $- 20 x$ .

$(3 - 4 x) (- 60 x + 23)$

Step 10

Factor.

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Step 10.1

Factor $- 1$ out of $- 60 x + 23$ .

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Step 10.1.1

Factor $- 1$ out of $- 60 x$ .

$(3 - 4 x) (- (60 x) + 23)$

Step 10.1.2

Rewrite $23$ as $- 1 (- 23)$ .

$(3 - 4 x) (- (60 x) - 1 (- 23))$

Step 10.1.3

Factor $- 1$ out of $- (60 x) - 1 (- 23)$ .

$(3 - 4 x) (- (60 x - 23))$

Step 10.2

Remove unnecessary parentheses.

$(3 - 4 x) \cdot - 1 (60 x - 23)$

Step 11

Factor out negative.

$- ((3 - 4 x) (60 x - 23))$

Step 12

Remove unnecessary parentheses.

$- (3 - 4 x) (60 x - 23)$