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

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

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

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

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

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

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

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

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

Apply the distributive property.

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x + 8 \cdot - 7 - (2 x + 3))$

Multiply $8$ by $- 7$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - (2 x + 3))$

Apply the distributive property.

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - (2 x) - 1 \cdot 3)$

Multiply $2$ by $- 1$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - 2 x - 1 \cdot 3)$

Multiply $- 1$ by $3$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - 2 x - 3)$

Subtract $2 x$ from $8 x$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (6 x - 56 - 3)$

Subtract $3$ from $- 56$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (6 x - 59)$