Factor 3(2x-3)^2(5x-6)+(2x-3)(5x-6)^2

$3 {(2 x - 3)}^{2} (5 x - 6) + (2 x - 3) {(5 x - 6)}^{2}$

Step 1

Factor $(2 x - 3) (5 x - 6)$ out of $3 {(2 x - 3)}^{2} (5 x - 6) + (2 x - 3) {(5 x - 6)}^{2}$ .

Factor $(2 x - 3) (5 x - 6)$ out of $3 {(2 x - 3)}^{2} (5 x - 6)$ .

$(2 x - 3) (5 x - 6) (3 (2 x - 3)) + (2 x - 3) {(5 x - 6)}^{2}$

Factor $(2 x - 3) (5 x - 6)$ out of $(2 x - 3) {(5 x - 6)}^{2}$ .

$(2 x - 3) (5 x - 6) (3 (2 x - 3)) + (2 x - 3) (5 x - 6) (5 x - 6)$

Factor $(2 x - 3) (5 x - 6)$ out of $(2 x - 3) (5 x - 6) (3 (2 x - 3)) + (2 x - 3) (5 x - 6) (5 x - 6)$ .

$(2 x - 3) (5 x - 6) (3 (2 x - 3) + 5 x - 6)$

Step 2

Apply the distributive property.

$(2 x - 3) (5 x - 6) (3 (2 x) + 3 \cdot - 3 + 5 x - 6)$

Step 3

Multiply $2$ by $3$ .

$(2 x - 3) (5 x - 6) (6 x + 3 \cdot - 3 + 5 x - 6)$

Step 4

Multiply $3$ by $- 3$ .

$(2 x - 3) (5 x - 6) (6 x - 9 + 5 x - 6)$

Step 5

Add $6 x$ and $5 x$ .

$(2 x - 3) (5 x - 6) (11 x - 9 - 6)$

Step 6

Subtract $6$ from $- 9$ .

$(2 x - 3) (5 x - 6) (11 x - 15)$