Algebra Examples

$2 a x - b y - a y + 2 b x$

Step 1

Regroup terms.

$- a y + 2 a x - b y + 2 b x$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(- a y + 2 a x) - b y + 2 b x$

Step 2.2

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $- 1 y + 2 x$ .

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

Step 4

Rewrite $- 1 y$ as $- y$ .

$(- y + 2 x) (a + b)$

Step 5

Factor $- 1$ out of $- y + 2 x$ .

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Step 5.1

Reorder $- y$ and $2 x$ .

$(2 x - y) (a + b)$

Step 5.2

Factor $- 1$ out of $2 x$ .

$(- (- 2 x) - y) (a + b)$

Step 5.3

Factor $- 1$ out of $- y$ .

$(- (- 2 x) - (y)) (a + b)$

Step 5.4

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

$- (- 2 x + y) (a + b)$

Step 6

Factor.

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Step 6.1

Factor $- 1$ out of $- 2 x + y$ .

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Step 6.1.1

Factor $- 1$ out of $- 2 x$ .

$- (- (2 x) + y) (a + b)$

Step 6.1.2

Factor $- 1$ out of $y$ .

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

Step 6.1.3

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

$- - (2 x - y) (a + b)$

Step 6.2

Remove unnecessary parentheses.

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

Step 7

Combine exponents.

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Step 7.1

Factor out negative.

$- ((- (2 x - y)) (a + b))$

Step 7.2

Multiply $- 1$ by $- 1$ .

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

Step 7.3

Multiply $2 x - y$ by $1$ .

$(2 x - y) (a + b)$