Algebra Examples

$\frac{1}{4} g^{2} (8 g + 12 h - 16 g h^{2})$

Step 1

Apply the distributive property.

$\frac{1}{4} \cdot (g^{2} (8 g) + g^{2} (12 h) + g^{2} (- 16 g h^{2}))$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{1}{4} \cdot (8 g^{2} g + g^{2} (12 h) + g^{2} (- 16 g h^{2}))$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{1}{4} \cdot (8 g^{2} g + 12 g^{2} h + g^{2} (- 16 g h^{2}))$

Step 2.3

Rewrite using the commutative property of multiplication.

$\frac{1}{4} \cdot (8 g^{2} g + 12 g^{2} h - 16 g^{2} (g h^{2}))$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $g$ .

$\frac{1}{4} \cdot (8 (g \cdot g^{2}) + 12 g^{2} h - 16 g^{2} (g h^{2}))$

Step 3.1.2

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

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Step 3.1.2.1

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

$\frac{1}{4} \cdot (8 (g^{1} g^{2}) + 12 g^{2} h - 16 g^{2} (g h^{2}))$

Step 3.1.2.2

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

$\frac{1}{4} \cdot (8 g^{1 + 2} + 12 g^{2} h - 16 g^{2} (g h^{2}))$

Step 3.1.3

Add $1$ and $2$ .

$\frac{1}{4} \cdot (8 g^{3} + 12 g^{2} h - 16 g^{2} (g h^{2}))$

Step 3.2

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

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Step 3.2.1

Move $g$ .

$\frac{1}{4} \cdot (8 g^{3} + 12 g^{2} h - 16 (g \cdot g^{2}) h^{2})$

Step 3.2.2

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

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Step 3.2.2.1

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

$\frac{1}{4} \cdot (8 g^{3} + 12 g^{2} h - 16 (g^{1} g^{2}) h^{2})$

Step 3.2.2.2

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

$\frac{1}{4} \cdot (8 g^{3} + 12 g^{2} h - 16 g^{1 + 2} h^{2})$

Step 3.2.3

Add $1$ and $2$ .

$\frac{1}{4} \cdot (8 g^{3} + 12 g^{2} h - 16 g^{3} h^{2})$

Step 4

Apply the distributive property.

$\frac{1}{4} (8 g^{3}) + \frac{1}{4} (12 g^{2} h) + \frac{1}{4} (- 16 g^{3} h^{2})$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $4$ .

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Step 5.1.1

Factor $4$ out of $8 g^{3}$ .

$\frac{1}{4} (4 (2 g^{3})) + \frac{1}{4} (12 g^{2} h) + \frac{1}{4} (- 16 g^{3} h^{2})$

Step 5.1.2

Cancel the common factor.

$\frac{1}{4} (4 (2 g^{3})) + \frac{1}{4} (12 g^{2} h) + \frac{1}{4} (- 16 g^{3} h^{2})$

Step 5.1.3

Rewrite the expression.

$2 g^{3} + \frac{1}{4} (12 g^{2} h) + \frac{1}{4} (- 16 g^{3} h^{2})$

Step 5.2

Cancel the common factor of $4$ .

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Step 5.2.1

Factor $4$ out of $12 g^{2} h$ .

$2 g^{3} + \frac{1}{4} (4 (3 g^{2} h)) + \frac{1}{4} (- 16 g^{3} h^{2})$

Step 5.2.2

Cancel the common factor.

$2 g^{3} + \frac{1}{4} (4 (3 g^{2} h)) + \frac{1}{4} (- 16 g^{3} h^{2})$

Step 5.2.3

Rewrite the expression.

$2 g^{3} + 3 g^{2} h + \frac{1}{4} (- 16 g^{3} h^{2})$

Step 5.3

Cancel the common factor of $4$ .

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Step 5.3.1

Factor $4$ out of $- 16 g^{3} h^{2}$ .

$2 g^{3} + 3 g^{2} h + \frac{1}{4} (4 (- 4 g^{3} h^{2}))$

Step 5.3.2

Cancel the common factor.

$2 g^{3} + 3 g^{2} h + \frac{1}{4} (4 (- 4 g^{3} h^{2}))$

Step 5.3.3

Rewrite the expression.

$2 g^{3} + 3 g^{2} h - 4 g^{3} h^{2}$