Factor (2x+5)(x-4)-(x-4)(5x+2)

$(2 x + 5) (x - 4) - (x - 4) (5 x + 2)$

Step 1

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

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

$(x - 4) (2 x + 5) - (x - 4) (5 x + 2)$

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

$(x - 4) (2 x + 5) + (x - 4) (- 1 (5 x + 2))$

Factor $x - 4$ out of $(x - 4) (2 x + 5) + (x - 4) (- 1 (5 x + 2))$ .

$(x - 4) (2 x + 5 - 1 (5 x + 2))$

Step 2

Apply the distributive property.

$(x - 4) (2 x + 5 - 1 (5 x) - 1 \cdot 2)$

Step 3

Multiply $5$ by $- 1$ .

$(x - 4) (2 x + 5 - 5 x - 1 \cdot 2)$

Step 4

Multiply $- 1$ by $2$ .

$(x - 4) (2 x + 5 - 5 x - 2)$

Step 5

Subtract $5 x$ from $2 x$ .

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

Step 6

Subtract $2$ from $5$ .

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

Step 7

Factor.

Factor $3$ out of $- 3 x + 3$ .

Factor $3$ out of $- 3 x$ .

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

Factor $3$ out of $3$ .

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

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

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

Remove unnecessary parentheses.

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

Step 8

Factor.

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

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

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

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

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

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

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

Remove unnecessary parentheses.

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

Step 9

Combine exponents.

Factor out negative.

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

Multiply $3$ by $- 1$ .

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

Step 10

Remove unnecessary parentheses.

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

Factor (2x+5)(x-4)-(x-4)(5x+2)

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