Factor 4(5x-8)^2+9(5x-8)(4x+9)

$4 {(5 x - 8)}^{2} + 9 (5 x - 8) (4 x + 9)$

Step 1

Factor $5 x - 8$ out of $4 {(5 x - 8)}^{2} + 9 (5 x - 8) (4 x + 9)$ .

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

$(5 x - 8) (4 (5 x - 8)) + 9 (5 x - 8) (4 x + 9)$

Factor $5 x - 8$ out of $9 (5 x - 8) (4 x + 9)$ .

$(5 x - 8) (4 (5 x - 8)) + (5 x - 8) (9 (4 x + 9))$

Factor $5 x - 8$ out of $(5 x - 8) (4 (5 x - 8)) + (5 x - 8) (9 (4 x + 9))$ .

$(5 x - 8) (4 (5 x - 8) + 9 (4 x + 9))$

Step 2

Apply the distributive property.

$(5 x - 8) (4 (5 x) + 4 \cdot - 8 + 9 (4 x + 9))$

Step 3

Multiply $5$ by $4$ .

$(5 x - 8) (20 x + 4 \cdot - 8 + 9 (4 x + 9))$

Step 4

Multiply $4$ by $- 8$ .

$(5 x - 8) (20 x - 32 + 9 (4 x + 9))$

Step 5

Apply the distributive property.

$(5 x - 8) (20 x - 32 + 9 (4 x) + 9 \cdot 9)$

Step 6

Multiply $4$ by $9$ .

$(5 x - 8) (20 x - 32 + 36 x + 9 \cdot 9)$

Step 7

Multiply $9$ by $9$ .

$(5 x - 8) (20 x - 32 + 36 x + 81)$

Step 8

Add $20 x$ and $36 x$ .

$(5 x - 8) (56 x - 32 + 81)$

Step 9

Add $- 32$ and $81$ .

$(5 x - 8) (56 x + 49)$

Step 10

Factor.

Factor $7$ out of $56 x + 49$ .

Factor $7$ out of $56 x$ .

$(5 x - 8) (7 (8 x) + 49)$

Factor $7$ out of $49$ .

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

Factor $7$ out of $7 (8 x) + 7 (7)$ .

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

Remove unnecessary parentheses.

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