Algebra Examples

$9 {(x + 7)}^{3} {(5 x + 8)}^{3} - {(x + 7)}^{2} {(5 x + 8)}^{4}$

Step 1

Factor ${(x + 7)}^{2} {(5 x + 8)}^{3}$ out of $9 {(x + 7)}^{3} {(5 x + 8)}^{3} - {(x + 7)}^{2} {(5 x + 8)}^{4}$ .

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Step 1.1

Factor ${(x + 7)}^{2} {(5 x + 8)}^{3}$ out of $9 {(x + 7)}^{3} {(5 x + 8)}^{3}$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 (x + 7)) - {(x + 7)}^{2} {(5 x + 8)}^{4}$

Step 1.2

Factor ${(x + 7)}^{2} {(5 x + 8)}^{3}$ out of $- {(x + 7)}^{2} {(5 x + 8)}^{4}$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 (x + 7)) + {(x + 7)}^{2} {(5 x + 8)}^{3} (- 1 (5 x + 8))$

Step 1.3

Factor ${(x + 7)}^{2} {(5 x + 8)}^{3}$ out of ${(x + 7)}^{2} {(5 x + 8)}^{3} (9 (x + 7)) + {(x + 7)}^{2} {(5 x + 8)}^{3} (- 1 (5 x + 8))$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 (x + 7) - 1 (5 x + 8))$

Step 2

Apply the distributive property.

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 x + 9 \cdot 7 - 1 (5 x + 8))$

Step 3

Multiply $9$ by $7$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 x + 63 - 1 (5 x + 8))$

Step 4

Apply the distributive property.

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 x + 63 - 1 (5 x) - 1 \cdot 8)$

Step 5

Multiply $5$ by $- 1$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 x + 63 - 5 x - 1 \cdot 8)$

Step 6

Multiply $- 1$ by $8$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (9 x + 63 - 5 x - 8)$

Step 7

Subtract $5 x$ from $9 x$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (4 x + 63 - 8)$

Step 8

Subtract $8$ from $63$ .

${(x + 7)}^{2} {(5 x + 8)}^{3} (4 x + 55)$