Factor (8(t-3)^7(4t+7)^8-8(4t+7)^7*4(t-3)^8)/(((4t+7)^8)^2)

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{8} - 8 {(4 t + 7)}^{7} \cdot 4 {(t - 3)}^{8}}{{({(4 t + 7)}^{8})}^{2}}$

Step 1

Factor $8 {(t - 3)}^{7} {(4 t + 7)}^{7}$ out of $8 {(t - 3)}^{7} {(4 t + 7)}^{8} - 8 {(4 t + 7)}^{7} \cdot (4 {(t - 3)}^{8})$ .

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

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (4 t + 7) - 8 {(4 t + 7)}^{7} \cdot (4 {(t - 3)}^{8})}{{({(4 t + 7)}^{8})}^{2}}$

Factor $8 {(t - 3)}^{7} {(4 t + 7)}^{7}$ out of $- 8 {(4 t + 7)}^{7} \cdot (4 {(t - 3)}^{8})$ .

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (4 t + 7) + 8 {(t - 3)}^{7} {(4 t + 7)}^{7} (- 1 \cdot (4 (t - 3)))}{{({(4 t + 7)}^{8})}^{2}}$

Factor $8 {(t - 3)}^{7} {(4 t + 7)}^{7}$ out of $8 {(t - 3)}^{7} {(4 t + 7)}^{7} (4 t + 7) + 8 {(t - 3)}^{7} {(4 t + 7)}^{7} (- 1 \cdot (4 (t - 3)))$ .

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (4 t + 7 - 1 \cdot (4 (t - 3)))}{{({(4 t + 7)}^{8})}^{2}}$

Step 2

Multiply $4$ by $- 1$ .

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (4 t + 7 - 4 (t - 3))}{{({(4 t + 7)}^{8})}^{2}}$

Step 3

Apply the distributive property.

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (4 t + 7 - 4 t - 4 \cdot - 3)}{{({(4 t + 7)}^{8})}^{2}}$

Step 4

Multiply $- 4$ by $- 3$ .

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (4 t + 7 - 4 t + 12)}{{({(4 t + 7)}^{8})}^{2}}$

Step 5

Subtract $4 t$ from $4 t$ .

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (0 + 7 + 12)}{{({(4 t + 7)}^{8})}^{2}}$

Step 6

Add $0$ and $7$ .

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} (7 + 12)}{{({(4 t + 7)}^{8})}^{2}}$

Step 7

Add $7$ and $12$ .

$\frac{8 {(t - 3)}^{7} {(4 t + 7)}^{7} \cdot 19}{{({(4 t + 7)}^{8})}^{2}}$

Step 8

Multiply $19$ by $8$ .

$\frac{152 {(t - 3)}^{7} {(4 t + 7)}^{7}}{{({(4 t + 7)}^{8})}^{2}}$

Factor (8(t-3)^7(4t+7)^8-8(4t+7)^7*4(t-3)^8)/(((4t+7)^8)^2)

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