Precalculus Examples

$\frac{6 a^{4} b^{3} + 3 a^{2} b^{2} - 12 a^{2} b}{3 a b}$

Step 1

Factor $3 a^{2} b$ out of $6 a^{4} b^{3} + 3 a^{2} b^{2} - 12 a^{2} b$ .

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Step 1.1

Factor $3 a^{2} b$ out of $6 a^{4} b^{3}$ .

$\frac{3 a^{2} b (2 a^{2} b^{2}) + 3 a^{2} b^{2} - 12 a^{2} b}{3 a b}$

Step 1.2

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

$\frac{3 a^{2} b (2 a^{2} b^{2}) + 3 a^{2} b (b) - 12 a^{2} b}{3 a b}$

Step 1.3

Factor $3 a^{2} b$ out of $- 12 a^{2} b$ .

$\frac{3 a^{2} b (2 a^{2} b^{2}) + 3 a^{2} b (b) + 3 a^{2} b (- 4)}{3 a b}$

Step 1.4

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

$\frac{3 a^{2} b (2 a^{2} b^{2} + b) + 3 a^{2} b (- 4)}{3 a b}$

Step 1.5

Factor $3 a^{2} b$ out of $3 a^{2} b (2 a^{2} b^{2} + b) + 3 a^{2} b (- 4)$ .

$\frac{3 a^{2} b (2 a^{2} b^{2} + b - 4)}{3 a b}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 a^{2} b (2 a^{2} b^{2} + b - 4)}{3 a b}$

Step 2.2

Rewrite the expression.

$\frac{a^{2} b (2 a^{2} b^{2} + b - 4)}{a b}$

Step 3

Cancel the common factor of $a^{2}$ and $a$ .

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Step 3.1

Factor $a$ out of $a^{2} b (2 a^{2} b^{2} + b - 4)$ .

$\frac{a (a b (2 a^{2} b^{2} + b - 4))}{a b}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $a b$ .

$\frac{a (a b (2 a^{2} b^{2} + b - 4))}{a (b)}$

Step 3.2.2

Cancel the common factor.

$\frac{a (a b (2 a^{2} b^{2} + b - 4))}{a b}$

Step 3.2.3

Rewrite the expression.

$\frac{a b (2 a^{2} b^{2} + b - 4)}{b}$

Step 4

Cancel the common factor of $b$ .

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Step 4.1

Cancel the common factor.

$\frac{a b (2 a^{2} b^{2} + b - 4)}{b}$

Step 4.2

Divide $a (2 a^{2} b^{2} + b - 4)$ by $1$ .

$a (2 a^{2} b^{2} + b - 4)$

Step 5

Apply the distributive property.

$a (2 a^{2} b^{2}) + a b + a \cdot - 4$

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

$2 a (a^{2} b^{2}) + a b + a \cdot - 4$

Step 6.2

Move $- 4$ to the left of $a$ .

$2 a (a^{2} b^{2}) + a b - 4 \cdot a$

Step 7

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 7.1

Move $a^{2}$ .

$2 (a^{2} a) b^{2} + a b - 4 \cdot a$

Step 7.2

Multiply $a^{2}$ by $a$ .

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Step 7.2.1

Raise $a$ to the power of $1$ .

$2 (a^{2} a^{1}) b^{2} + a b - 4 \cdot a$

Step 7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 a^{2 + 1} b^{2} + a b - 4 \cdot a$

Step 7.3

Add $2$ and $1$ .

$2 a^{3} b^{2} + a b - 4 \cdot a$

$2 a^{3} b^{2} + a b - 4 a$