Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $2$ by $5$ .

${(x + 8)}^{3} {(2 x + 9)}^{3} (10 x + 5 \cdot 9 - (x + 8))$

Step 4

Multiply $5$ by $9$ .

${(x + 8)}^{3} {(2 x + 9)}^{3} (10 x + 45 - (x + 8))$

Step 5

Apply the distributive property.

${(x + 8)}^{3} {(2 x + 9)}^{3} (10 x + 45 - x - 1 \cdot 8)$

Step 6

Multiply $- 1$ by $8$ .

${(x + 8)}^{3} {(2 x + 9)}^{3} (10 x + 45 - x - 8)$

Step 7

Subtract $x$ from $10 x$ .

${(x + 8)}^{3} {(2 x + 9)}^{3} (9 x + 45 - 8)$

Step 8

Subtract $8$ from $45$ .

${(x + 8)}^{3} {(2 x + 9)}^{3} (9 x + 37)$