Algebra Examples

$(x + 9) (x - 2) - 9 x - 6$

Step 1

Factor $- 1$ out of $(x + 9) (x - 2) - 9 x - 6$ .

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Step 1.1

Factor $- 1$ out of $(x + 9) (x - 2)$ .

$- ((- x - 9) (x - 2)) - 9 x - 6$

Step 1.2

Factor $- 1$ out of $- 9 x$ .

$- ((- x - 9) (x - 2)) - (9 x) - 6$

Step 1.3

Rewrite $- 6$ as $- 1 (6)$ .

$- ((- x - 9) (x - 2)) - (9 x) - 1 (6)$

Step 1.4

Factor $- 1$ out of $- ((- x - 9) (x - 2)) - (9 x)$ .

$- ((- x - 9) (x - 2) + 9 x) - 1 (6)$

Step 1.5

Factor $- 1$ out of $- ((- x - 9) (x - 2) + 9 x) - 1 (6)$ .

$- ((- x - 9) (x - 2) + 9 x + 6)$

Step 2

Expand $(- x - 9) (x - 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- (- x (x - 2) - 9 (x - 2) + 9 x + 6)$

Step 2.2

Apply the distributive property.

$- (- x \cdot x - x \cdot - 2 - 9 (x - 2) + 9 x + 6)$

Step 2.3

Apply the distributive property.

$- (- x \cdot x - x \cdot - 2 - 9 x - 9 \cdot - 2 + 9 x + 6)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.1.1

Move $x$ .

$- (- (x \cdot x) - x \cdot - 2 - 9 x - 9 \cdot - 2 + 9 x + 6)$

Step 3.1.1.2

Multiply $x$ by $x$ .

$- (- x^{2} - x \cdot - 2 - 9 x - 9 \cdot - 2 + 9 x + 6)$

Step 3.1.2

Multiply $- 2$ by $- 1$ .

$- (- x^{2} + 2 x - 9 x - 9 \cdot - 2 + 9 x + 6)$

Step 3.1.3

Multiply $- 9$ by $- 2$ .

$- (- x^{2} + 2 x - 9 x + 18 + 9 x + 6)$

Step 3.2

Subtract $9 x$ from $2 x$ .

$- (- x^{2} - 7 x + 18 + 9 x + 6)$

Step 4

Add $- 7 x$ and $9 x$ .

$- (- x^{2} + 2 x + 18 + 6)$

Step 5

Add $18$ and $6$ .

$- (- x^{2} + 2 x + 24)$

Step 6

Factor.

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Step 6.1

Factor by grouping.

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Step 6.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 1 \cdot 24 = - 24$ and whose sum is $b = 2$ .

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Step 6.1.1.1

Factor $2$ out of $2 x$ .

$- (- x^{2} + 2 (x) + 24)$

Step 6.1.1.2

Rewrite $2$ as $- 4$ plus $6$

$- (- x^{2} + (- 4 + 6) x + 24)$

Step 6.1.1.3

Apply the distributive property.

$- (- x^{2} - 4 x + 6 x + 24)$

Step 6.1.2

Factor out the greatest common factor from each group.

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Step 6.1.2.1

Group the first two terms and the last two terms.

$- ((- x^{2} - 4 x) + 6 x + 24)$

Step 6.1.2.2

Factor out the greatest common factor (GCF) from each group.

$- (x (- x - 4) - 6 (- x - 4))$

Step 6.1.3

Factor the polynomial by factoring out the greatest common factor, $- x - 4$ .

$- ((- x - 4) (x - 6))$

Step 6.2

Remove unnecessary parentheses.

$- (- x - 4) (x - 6)$

Step 7

Factor.

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Step 7.1

Factor $- 1$ out of $- x - 4$ .

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Step 7.1.1

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

$- (- (x) - 4) (x - 6)$

Step 7.1.2

Rewrite $- 4$ as $- 1 (4)$ .

$- (- (x) - 1 (4)) (x - 6)$

Step 7.1.3

Factor $- 1$ out of $- (x) - 1 (4)$ .

$- - (x + 4) (x - 6)$

Step 7.2

Remove unnecessary parentheses.

$- - 1 (x + 4) (x - 6)$

Step 8

Combine exponents.

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Step 8.1

Factor out negative.

$- ((- (x + 4)) (x - 6))$

Step 8.2

Multiply $- 1$ by $- 1$ .

$1 ((x + 4) (x - 6))$

Step 8.3

Multiply $x + 4$ by $1$ .

$(x + 4) (x - 6)$