Algebra Examples

$6 {(x + 6)}^{2} {(2 x - 5)}^{2} - (x + 6) {(2 x - 5)}^{3}$

Step 1

Factor $(x + 6) {(2 x - 5)}^{2}$ out of $6 {(x + 6)}^{2} {(2 x - 5)}^{2} - (x + 6) {(2 x - 5)}^{3}$ .

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Step 1.1

Factor $(x + 6) {(2 x - 5)}^{2}$ out of $6 {(x + 6)}^{2} {(2 x - 5)}^{2}$ .

$(x + 6) {(2 x - 5)}^{2} (6 (x + 6)) - (x + 6) {(2 x - 5)}^{3}$

Step 1.2

Factor $(x + 6) {(2 x - 5)}^{2}$ out of $- (x + 6) {(2 x - 5)}^{3}$ .

$(x + 6) {(2 x - 5)}^{2} (6 (x + 6)) + (x + 6) {(2 x - 5)}^{2} (- 1 (2 x - 5))$

Step 1.3

Factor $(x + 6) {(2 x - 5)}^{2}$ out of $(x + 6) {(2 x - 5)}^{2} (6 (x + 6)) + (x + 6) {(2 x - 5)}^{2} (- 1 (2 x - 5))$ .

$(x + 6) {(2 x - 5)}^{2} (6 (x + 6) - 1 (2 x - 5))$

Step 2

Apply the distributive property.

$(x + 6) {(2 x - 5)}^{2} (6 x + 6 \cdot 6 - 1 (2 x - 5))$

Step 3

Multiply $6$ by $6$ .

$(x + 6) {(2 x - 5)}^{2} (6 x + 36 - 1 (2 x - 5))$

Step 4

Apply the distributive property.

$(x + 6) {(2 x - 5)}^{2} (6 x + 36 - 1 (2 x) - 1 \cdot - 5)$

Step 5

Multiply $2$ by $- 1$ .

$(x + 6) {(2 x - 5)}^{2} (6 x + 36 - 2 x - 1 \cdot - 5)$

Step 6

Multiply $- 1$ by $- 5$ .

$(x + 6) {(2 x - 5)}^{2} (6 x + 36 - 2 x + 5)$

Step 7

Subtract $2 x$ from $6 x$ .

$(x + 6) {(2 x - 5)}^{2} (4 x + 36 + 5)$

Step 8

Add $36$ and $5$ .

$(x + 6) {(2 x - 5)}^{2} (4 x + 41)$