Algebra Examples

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

Step 1

Factor by grouping.

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Step 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 $a \cdot c = 1 \cdot 9 = 9$ and whose sum is $b = - 6$ .

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Step 1.1.1

Reorder terms.

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

Step 1.1.2

Reorder $9 {(a + b)}^{2}$ and $- 6 x (a + b)$ .

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

Step 1.1.3

Factor $- 6$ out of $- 6 x (a + b)$ .

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

Step 1.1.4

Rewrite $- 6$ as $- 3$ plus $- 3$

$x^{2} + (- 3 - 3) (x (a + b)) + 9 {(a + b)}^{2}$

Step 1.1.5

Apply the distributive property.

$x^{2} - 3 (x (a + b)) - 3 (x (a + b)) + 9 {(a + b)}^{2}$

Step 1.1.6

Remove unnecessary parentheses.

$x^{2} - 3 x (a + b) - 3 (x (a + b)) + 9 {(a + b)}^{2}$

Step 1.1.7

Remove unnecessary parentheses.

$x^{2} - 3 x (a + b) - 3 x (a + b) + 9 {(a + b)}^{2}$

Step 1.2

Factor out the greatest common factor from each group.

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Step 1.2.1

Group the first two terms and the last two terms.

$(x^{2} - 3 x (a + b)) - 3 x (a + b) + 9 {(a + b)}^{2}$

Step 1.2.2

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

$x (x - 3 (a + b)) - 3 (a + b) (x - 3 (a + b))$

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $x - 3 (a + b)$ .

$(x - 3 (a + b)) (x - 3 (a + b))$

Step 2

Apply the distributive property.

$(x - 3 a - 3 b) (x - 3 (a + b))$

Step 3

Apply the distributive property.

$(x - 3 a - 3 b) (x - 3 a - 3 b)$