Algebra Examples

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

Step 1

Regroup terms.

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

Step 2

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

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Step 2.1

Factor $a$ out of $3 a x$ .

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

Step 2.2

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

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

Step 2.3

Factor $a$ out of $- a z$ .

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

Step 2.4

Factor $a$ out of $a (3 x) + a (2 y)$ .

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

Step 2.5

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

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

Step 3

Rewrite $- 1 z$ as $- z$ .

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

Step 4

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

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Step 4.1

Factor $b$ out of $3 b x$ .

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

Step 4.2

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

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

Step 4.3

Factor $b$ out of $- b z$ .

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

Step 4.4

Factor $b$ out of $b (3 x) + b (2 y)$ .

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

Step 4.5

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

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

Step 5

Rewrite $- 1 z$ as $- z$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

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