Algebra Examples

$a^{2} - x y - a x + a y$

Step 1

Regroup terms.

$- a x + a^{2} - x y + a y$

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.

$(- a x + a^{2}) - x y + a y$

Step 2.2

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

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

Step 3

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

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

Step 4

Rewrite $- 1 x$ as $- x$ .

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

Step 5

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

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Step 5.1

Reorder $- x$ and $a$ .

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

Step 5.2

Factor $- 1$ out of $a$ .

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

Step 5.3

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

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

Step 5.4

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

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

Step 5.5

Rewrite $- 1 (- a + x)$ as $- (- a + x)$ .

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

Step 6

Factor.

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Step 6.1

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

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Step 6.1.1

Factor $- 1$ out of $- a$ .

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

Step 6.1.2

Factor $- 1$ out of $x$ .

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

Step 6.1.3

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

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

Step 6.2

Remove unnecessary parentheses.

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

Step 7

Combine exponents.

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Step 7.1

Factor out negative.

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

Step 7.2

Multiply $- 1$ by $- 1$ .

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

Step 7.3

Multiply $a - x$ by $1$ .

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