Basic Math Examples

$a c - b c + b - a - b y + a y$

Step 1

Regroup terms.

$- b y + a y + a c - b c + b - a$

Step 2

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

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Step 2.1

Reorder $- b y$ and $a y$ .

$a y - b y + a c - b c + b - a$

Step 2.2

Factor $- y$ out of $a y$ .

$- y (- a) - b y + a c - b c + b - a$

Step 2.3

Factor $- y$ out of $- b y$ .

$- y (- a) - y (b) + a c - b c + b - a$

Step 2.4

Factor $- y$ out of $- y (- a) - y (b)$ .

$- y (- a + b) + a c - b c + b - a$

Step 3

Reorder terms.

$- y (- a + b) - a + b + a c - b c$

Step 4

Factor out the greatest common factor from each group.

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Step 4.1

Group the first two terms and the last two terms.

$- y (- a + b) + (- a + b) + a c - b c$

Step 4.2

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

$- y (- a + b) + 1 (- a + b) - c (- a + b)$

Step 5

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

$- y (- a + b) + (- a + b) (1 - c)$

Step 6

Factor $- a + b$ out of $- y (- a + b) + (- a + b) (1 - c)$ .

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Step 6.1

Factor $- a + b$ out of $- y (- a + b)$ .

$(- a + b) (- y) + (- a + b) (1 - c)$

Step 6.2

Factor $- a + b$ out of $(- a + b) (- y) + (- a + b) (1 - c)$ .

$(- a + b) (- y + 1 - c)$

Step 7

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

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Step 7.1

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

$(- (a) + b) (- y + 1 - c)$

Step 7.2

Factor $- 1$ out of $b$ .

$(- (a) - 1 (- b)) (- y + 1 - c)$

Step 7.3

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

$- (a - b) (- y + 1 - c)$

Step 8

Factor.

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Step 8.1

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

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Step 8.1.1

Reorder the expression.

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Step 8.1.1.1

Move $1$ .

$- (a - b) (- y - c + 1)$

Step 8.1.1.2

Reorder $- y$ and $- c$ .

$- (a - b) (- c - y + 1)$

Step 8.1.2

Factor $- 1$ out of $- c$ .

$- (a - b) (- (c) - y + 1)$

Step 8.1.3

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

$- (a - b) (- (c) - (y) + 1)$

Step 8.1.4

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

$- (a - b) (- (c) - (y) - 1 (- 1))$

Step 8.1.5

Factor $- 1$ out of $- (c) - (y)$ .

$- (a - b) (- (c + y) - 1 (- 1))$

Step 8.1.6

Factor $- 1$ out of $- (c + y) - 1 (- 1)$ .

$- (a - b) (- (c + y - 1))$

Step 8.2

Remove unnecessary parentheses.

$- (a - b) \cdot - 1 (c + y - 1)$

Step 9

Combine exponents.

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Step 9.1

Factor out negative.

$- ((a - b) \cdot - 1 (c + y - 1))$

Step 9.2

Multiply $- 1$ by $- 1$ .

$1 ((a - b) (c + y - 1))$

Step 9.3

Multiply $a - b$ by $1$ .

$(a - b) (c + y - 1)$