Algebra Examples

$2 (x - 2) {(x + 1)}^{2} - 3 {(x - 2)}^{2} (x + 1)$

Step 1

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

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Step 1.1

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

$(x - 2) (x + 1) (2 (x + 1)) - 3 {(x - 2)}^{2} (x + 1)$

Step 1.2

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

$(x - 2) (x + 1) (2 (x + 1)) + (x - 2) (x + 1) (- 3 (x - 2))$

Step 1.3

Factor $(x - 2) (x + 1)$ out of $(x - 2) (x + 1) (2 (x + 1)) + (x - 2) (x + 1) (- 3 (x - 2))$ .

$(x - 2) (x + 1) (2 (x + 1) - 3 (x - 2))$

Step 2

Apply the distributive property.

$(x - 2) (x + 1) (2 x + 2 \cdot 1 - 3 (x - 2))$

Step 3

Multiply $2$ by $1$ .

$(x - 2) (x + 1) (2 x + 2 - 3 (x - 2))$

Step 4

Apply the distributive property.

$(x - 2) (x + 1) (2 x + 2 - 3 x - 3 \cdot - 2)$

Step 5

Multiply $- 3$ by $- 2$ .

$(x - 2) (x + 1) (2 x + 2 - 3 x + 6)$

Step 6

Subtract $3 x$ from $2 x$ .

$(x - 2) (x + 1) (- x + 2 + 6)$

Step 7

Add $2$ and $6$ .

$(x - 2) (x + 1) (- x + 8)$

Step 8

Factor.

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Step 8.1

Factor $- 1$ out of $- x + 8$ .

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Step 8.1.1

Factor $- 1$ out of $- x$ .

$(x - 2) (x + 1) (- (x) + 8)$

Step 8.1.2

Rewrite $8$ as $- 1 (- 8)$ .

$(x - 2) (x + 1) (- (x) - 1 (- 8))$

Step 8.1.3

Factor $- 1$ out of $- (x) - 1 (- 8)$ .

$(x - 2) (x + 1) (- (x - 8))$

Step 8.2

Remove unnecessary parentheses.

$(x - 2) (x + 1) \cdot - 1 (x - 8)$

Step 9

Factor out negative.

$- ((x - 2) (x + 1) (x - 8))$

Step 10

Remove unnecessary parentheses.

$- (x - 2) (x + 1) (x - 8)$