Algebra Examples

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

Step 1

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

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Step 1.1

Reorder the expression.

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Step 1.1.1

Reorder $1$ and $- x$ .

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

Step 1.1.2

Move $1$ .

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

Step 1.1.3

Reorder $- x$ and $2 a (- x + 1)$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 2

Apply the distributive property.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $- 2$ by $1$ .

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

Step 5

Multiply $- 2$ by $- 1$ .

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

Step 6

Factor.

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Step 6.1

Rewrite $2 a x - 2 a + x - 1$ in a factored form.

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Step 6.1.1

Factor out the greatest common factor from each group.

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Step 6.1.1.1

Group the first two terms and the last two terms.

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

Step 6.1.1.2

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

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

Step 6.1.2

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

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

Step 6.2

Remove unnecessary parentheses.

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