Factor 3a^3-3a^2b+9ab^2-a^2+ab-3b^2

$3 a^{3} - 3 a^{2} b + 9 a b^{2} - a^{2} + a b - 3 b^{2}$

Step 1

Regroup terms.

$3 a^{3} - a^{2} - 3 a^{2} b + 9 a b^{2} + a b - 3 b^{2}$

Step 2

Factor $a^{2}$ out of $3 a^{3} - a^{2}$ .

Factor $a^{2}$ out of $3 a^{3}$ .

$a^{2} (3 a) - a^{2} - 3 a^{2} b + 9 a b^{2} + a b - 3 b^{2}$

Factor $a^{2}$ out of $- a^{2}$ .

$a^{2} (3 a) + a^{2} \cdot - 1 - 3 a^{2} b + 9 a b^{2} + a b - 3 b^{2}$

Factor $a^{2}$ out of $a^{2} (3 a) + a^{2} \cdot - 1$ .

$a^{2} (3 a - 1) - 3 a^{2} b + 9 a b^{2} + a b - 3 b^{2}$

Step 3

Factor $b$ out of $- 3 a^{2} b + 9 a b^{2} + a b - 3 b^{2}$ .

Factor $b$ out of $- 3 a^{2} b$ .

$a^{2} (3 a - 1) + b (- 3 a^{2}) + 9 a b^{2} + a b - 3 b^{2}$

Factor $b$ out of $9 a b^{2}$ .

$a^{2} (3 a - 1) + b (- 3 a^{2}) + b (9 a b) + a b - 3 b^{2}$

Factor $b$ out of $a b$ .

$a^{2} (3 a - 1) + b (- 3 a^{2}) + b (9 a b) + b a - 3 b^{2}$

Factor $b$ out of $- 3 b^{2}$ .

$a^{2} (3 a - 1) + b (- 3 a^{2}) + b (9 a b) + b a + b (- 3 b)$

Factor $b$ out of $b (- 3 a^{2}) + b (9 a b)$ .

$a^{2} (3 a - 1) + b (- 3 a^{2} + 9 a b) + b a + b (- 3 b)$

Factor $b$ out of $b (- 3 a^{2} + 9 a b) + b a$ .

$a^{2} (3 a - 1) + b (- 3 a^{2} + 9 a b + a) + b (- 3 b)$

Factor $b$ out of $b (- 3 a^{2} + 9 a b + a) + b (- 3 b)$ .

$a^{2} (3 a - 1) + b (- 3 a^{2} + 9 a b + a - 3 b)$

Step 4

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$a^{2} (3 a - 1) + b ((- 3 a^{2} + 9 a b) + a - 3 b)$

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

$a^{2} (3 a - 1) + b (3 a (- a + 3 b) - 1 (- a + 3 b))$

Step 5

Factor.

Factor the polynomial by factoring out the greatest common factor, $- a + 3 b$ .

$a^{2} (3 a - 1) + b ((- a + 3 b) (3 a - 1))$

Remove unnecessary parentheses.

$a^{2} (3 a - 1) + b (- a + 3 b) (3 a - 1)$

Step 6

Factor $3 a - 1$ out of $a^{2} (3 a - 1) + b (- a + 3 b) (3 a - 1)$ .

Factor $3 a - 1$ out of $a^{2} (3 a - 1)$ .

$(3 a - 1) a^{2} + b (- a + 3 b) (3 a - 1)$

Factor $3 a - 1$ out of $b (- a + 3 b) (3 a - 1)$ .

$(3 a - 1) a^{2} + (3 a - 1) (b (- a + 3 b))$

Factor $3 a - 1$ out of $(3 a - 1) a^{2} + (3 a - 1) (b (- a + 3 b))$ .

$(3 a - 1) (a^{2} + b (- a + 3 b))$

Step 7

Apply the distributive property.

$(3 a - 1) (a^{2} + b (- a) + b (3 b))$

Step 8

Rewrite using the commutative property of multiplication.

$(3 a - 1) (a^{2} - b a + b (3 b))$

Step 9

Rewrite using the commutative property of multiplication.

$(3 a - 1) (a^{2} - b a + 3 b \cdot b)$

Step 10

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$(3 a - 1) (a^{2} - b a + 3 (b \cdot b))$

Multiply $b$ by $b$ .

$(3 a - 1) (a^{2} - b a + 3 b^{2})$

Factor 3a^3-3a^2b+9ab^2-a^2+ab-3b^2

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