Algebra Examples

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

Step 1

Regroup terms.

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

Step 2

Factor $- b$ out of $- b y^{2} + a b$ .

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Step 2.1

Factor $- b$ out of $- b y^{2}$ .

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

Step 2.2

Factor $- b$ out of $a b$ .

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

Step 2.3

Factor $- b$ out of $- b (y^{2}) - b (- a)$ .

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

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

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

Step 3.2

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

$- b (y^{2} - a) + x (y^{2} - a) + 1 (y^{2} - a)$

Step 4

Factor the polynomial by factoring out the greatest common factor, $y^{2} - a$ .

$- b (y^{2} - a) + (y^{2} - a) (x + 1)$

Step 5

Factor $y^{2} - a$ out of $- b (y^{2} - a) + (y^{2} - a) (x + 1)$ .

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Step 5.1

Factor $y^{2} - a$ out of $- b (y^{2} - a)$ .

$(y^{2} - a) (- b) + (y^{2} - a) (x + 1)$

Step 5.2

Factor $y^{2} - a$ out of $(y^{2} - a) (- b) + (y^{2} - a) (x + 1)$ .

$(y^{2} - a) (- b + x + 1)$

Step 6

Factor.

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Step 6.1

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

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Step 6.1.1

Factor $- 1$ out of $- b$ .

$(y^{2} - a) (- (b) + x + 1)$

Step 6.1.2

Factor $- 1$ out of $x$ .

$(y^{2} - a) (- (b) - 1 (- x) + 1)$

Step 6.1.3

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

$(y^{2} - a) (- (b) - 1 (- x) - 1 (- 1))$

Step 6.1.4

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

$(y^{2} - a) (- (b - x) - 1 (- 1))$

Step 6.1.5

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

$(y^{2} - a) (- (b - x - 1))$

Step 6.2

Remove unnecessary parentheses.

$(y^{2} - a) \cdot - 1 (b - x - 1)$

Step 7

Factor out negative.

$- ((y^{2} - a) (b - x - 1))$

Step 8

Remove unnecessary parentheses.

$- (y^{2} - a) (b - x - 1)$