Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $8$ by $- 7$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $2$ by $- 1$ .

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

Step 6

Multiply $- 1$ by $3$ .

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

Step 7

Subtract $2 x$ from $8 x$ .

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

Step 8

Subtract $3$ from $- 56$ .

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