Factor 5(3x-4)^2+3(3x-4)(7x-8)

$5 {(3 x - 4)}^{2} + 3 (3 x - 4) (7 x - 8)$

Step 1

Factor $3 x - 4$ out of $5 {(3 x - 4)}^{2} + 3 (3 x - 4) (7 x - 8)$ .

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

$(3 x - 4) (5 (3 x - 4)) + 3 (3 x - 4) (7 x - 8)$

Factor $3 x - 4$ out of $3 (3 x - 4) (7 x - 8)$ .

$(3 x - 4) (5 (3 x - 4)) + (3 x - 4) (3 (7 x - 8))$

Factor $3 x - 4$ out of $(3 x - 4) (5 (3 x - 4)) + (3 x - 4) (3 (7 x - 8))$ .

$(3 x - 4) (5 (3 x - 4) + 3 (7 x - 8))$

Step 2

Apply the distributive property.

$(3 x - 4) (5 (3 x) + 5 \cdot - 4 + 3 (7 x - 8))$

Step 3

Multiply $3$ by $5$ .

$(3 x - 4) (15 x + 5 \cdot - 4 + 3 (7 x - 8))$

Step 4

Multiply $5$ by $- 4$ .

$(3 x - 4) (15 x - 20 + 3 (7 x - 8))$

Step 5

Apply the distributive property.

$(3 x - 4) (15 x - 20 + 3 (7 x) + 3 \cdot - 8)$

Step 6

Multiply $7$ by $3$ .

$(3 x - 4) (15 x - 20 + 21 x + 3 \cdot - 8)$

Step 7

Multiply $3$ by $- 8$ .

$(3 x - 4) (15 x - 20 + 21 x - 24)$

Step 8

Add $15 x$ and $21 x$ .

$(3 x - 4) (36 x - 20 - 24)$

Step 9

Subtract $24$ from $- 20$ .

$(3 x - 4) (36 x - 44)$

Step 10

Factor.

Factor $4$ out of $36 x - 44$ .

Factor $4$ out of $36 x$ .

$(3 x - 4) (4 (9 x) - 44)$

Factor $4$ out of $- 44$ .

$(3 x - 4) (4 (9 x) + 4 (- 11))$

Factor $4$ out of $4 (9 x) + 4 (- 11)$ .

$(3 x - 4) (4 (9 x - 11))$

Remove unnecessary parentheses.

$(3 x - 4) \cdot 4 (9 x - 11)$