Algebra Examples

$4 (x^{2} - 2 x) - 2 (x^{2} - 3)$

Step 1

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

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Step 1.1

Factor $2$ out of $4 (x^{2} - 2 x)$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $- 2$ by $2$ .

$2 (2 x^{2} - 4 x - (x^{2} - 3))$

Step 4

Apply the distributive property.

$2 (2 x^{2} - 4 x - x^{2} - - 3)$

Step 5

Multiply $- 1$ by $- 3$ .

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

Step 6

Subtract $x^{2}$ from $2 x^{2}$ .

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

Step 7

Factor.

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Step 7.1

Factor $x^{2} - 4 x + 3$ using the AC method.

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Step 7.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $- 4$ .

$- 3, - 1$

Step 7.1.2

Write the factored form using these integers.

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

Step 7.2

Remove unnecessary parentheses.

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