Algebra Examples

$5 a x - 2 a y - 3 b z + 2 b y + 3 a z - 5 b x$

Step 1

Regroup terms.

$- 2 a y + 2 b y + 5 a x - 3 b z + 3 a z - 5 b x$

Step 2

Factor $- 2 y$ out of $- 2 a y + 2 b y$ .

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Step 2.1

Factor $- 2 y$ out of $- 2 a y$ .

$- 2 y (a) + 2 b y + 5 a x - 3 b z + 3 a z - 5 b x$

Step 2.2

Factor $- 2 y$ out of $2 b y$ .

$- 2 y (a) - 2 y (- b) + 5 a x - 3 b z + 3 a z - 5 b x$

Step 2.3

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

$- 2 y (a - b) + 5 a x - 3 b z + 3 a z - 5 b x$

Step 3

Regroup terms.

$- 2 y (a - b) + 3 a z + 5 a x - 3 b z - 5 b x$

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.

$- 2 y (a - b) + (3 a z + 5 a x) - 3 b z - 5 b x$

Step 4.2

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

$- 2 y (a - b) + a (3 z + 5 x) - b (3 z + 5 x)$

Step 5

Factor the polynomial by factoring out the greatest common factor, $3 z + 5 x$ .

$- 2 y (a - b) + (3 z + 5 x) (a - b)$

Step 6

Factor $a - b$ out of $- 2 y (a - b) + (3 z + 5 x) (a - b)$ .

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Step 6.1

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

$(a - b) (- 2 y) + (3 z + 5 x) (a - b)$

Step 6.2

Factor $a - b$ out of $(3 z + 5 x) (a - b)$ .

$(a - b) (- 2 y) + (a - b) (3 z + 5 x)$

Step 6.3

Factor $a - b$ out of $(a - b) (- 2 y) + (a - b) (3 z + 5 x)$ .

$(a - b) (- 2 y + 3 z + 5 x)$

Step 7

Factor.

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Step 7.1

Factor $- 1$ out of $- 2 y + 3 z + 5 x$ .

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Step 7.1.1

Reorder the expression.

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Step 7.1.1.1

Move $3 z$ .

$(a - b) (- 2 y + 5 x + 3 z)$

Step 7.1.1.2

Reorder $- 2 y$ and $5 x$ .

$(a - b) (5 x - 2 y + 3 z)$

Step 7.1.2

Factor $- 1$ out of $5 x$ .

$(a - b) (- (- 5 x) - 2 y + 3 z)$

Step 7.1.3

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

$(a - b) (- (- 5 x) - (2 y) + 3 z)$

Step 7.1.4

Factor $- 1$ out of $3 z$ .

$(a - b) (- (- 5 x) - (2 y) - (- 3 z))$

Step 7.1.5

Factor $- 1$ out of $- (- 5 x) - (2 y)$ .

$(a - b) (- (- 5 x + 2 y) - (- 3 z))$

Step 7.1.6

Factor $- 1$ out of $- (- 5 x + 2 y) - (- 3 z)$ .

$(a - b) (- (- 5 x + 2 y - 3 z))$

Step 7.2

Remove unnecessary parentheses.

$(a - b) \cdot - 1 (- 5 x + 2 y - 3 z)$

Step 8

Factor out negative.

$- ((a - b) (- 5 x + 2 y - 3 z))$

Step 9

Remove unnecessary parentheses.

$- (a - b) (- 5 x + 2 y - 3 z)$

Step 10

Factor.

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Step 10.1

Factor $- 1$ out of $- 5 x + 2 y - 3 z$ .

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Step 10.1.1

Factor $- 1$ out of $- 5 x$ .

$- (a - b) (- (5 x) + 2 y - 3 z)$

Step 10.1.2

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

$- (a - b) (- (5 x) - (- 2 y) - 3 z)$

Step 10.1.3

Factor $- 1$ out of $- 3 z$ .

$- (a - b) (- (5 x) - (- 2 y) - (3 z))$

Step 10.1.4

Factor $- 1$ out of $- (5 x) - (- 2 y)$ .

$- (a - b) (- (5 x - 2 y) - (3 z))$

Step 10.1.5

Factor $- 1$ out of $- (5 x - 2 y) - (3 z)$ .

$- (a - b) (- (5 x - 2 y + 3 z))$

Step 10.2

Remove unnecessary parentheses.

$- (a - b) \cdot - 1 (5 x - 2 y + 3 z)$

Step 11

Combine exponents.

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Step 11.1

Factor out negative.

$- ((a - b) \cdot - 1 (5 x - 2 y + 3 z))$

Step 11.2

Multiply $- 1$ by $- 1$ .

$1 ((a - b) (5 x - 2 y + 3 z))$

Step 11.3

Multiply $a - b$ by $1$ .

$(a - b) (5 x - 2 y + 3 z)$