Basic Math Examples

$\frac{1}{2} \cdot (u v^{2} (10 u^{2} - 4 u v + 8 v^{2}))$

Step 1

Apply the distributive property.

$\frac{1}{2} \cdot (u v^{2} (10 u^{2}) + u v^{2} (- 4 u v) + u v^{2} (8 v^{2}))$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot (10 u v^{2} u^{2} + u v^{2} (- 4 u v) + u v^{2} (8 v^{2}))$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot (10 u v^{2} u^{2} - 4 u v^{2} (u v) + u v^{2} (8 v^{2}))$

Step 2.3

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot (10 u v^{2} u^{2} - 4 u v^{2} (u v) + 8 u v^{2} v^{2})$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $u^{2}$ .

$\frac{1}{2} \cdot (10 (u^{2} u) v^{2} - 4 u v^{2} (u v) + 8 u v^{2} v^{2})$

Step 3.1.2

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

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Step 3.1.2.1

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

$\frac{1}{2} \cdot (10 (u^{2} u^{1}) v^{2} - 4 u v^{2} (u v) + 8 u v^{2} v^{2})$

Step 3.1.2.2

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

$\frac{1}{2} \cdot (10 u^{2 + 1} v^{2} - 4 u v^{2} (u v) + 8 u v^{2} v^{2})$

Step 3.1.3

Add $2$ and $1$ .

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u v^{2} (u v) + 8 u v^{2} v^{2})$

Step 3.2

Multiply $u$ by $u$ by adding the exponents.

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Step 3.2.1

Move $u$ .

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 (u \cdot u) v^{2} v + 8 u v^{2} v^{2})$

Step 3.2.2

Multiply $u$ by $u$ .

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} v^{2} v + 8 u v^{2} v^{2})$

Step 3.3

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

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Step 3.3.1

Move $v$ .

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} (v \cdot v^{2}) + 8 u v^{2} v^{2})$

Step 3.3.2

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

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Step 3.3.2.1

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

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} (v^{1} v^{2}) + 8 u v^{2} v^{2})$

Step 3.3.2.2

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

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} v^{1 + 2} + 8 u v^{2} v^{2})$

Step 3.3.3

Add $1$ and $2$ .

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} v^{3} + 8 u v^{2} v^{2})$

Step 3.4

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

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Step 3.4.1

Move $v^{2}$ .

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} v^{3} + 8 u (v^{2} v^{2}))$

Step 3.4.2

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

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} v^{3} + 8 u v^{2 + 2})$

Step 3.4.3

Add $2$ and $2$ .

$\frac{1}{2} \cdot (10 u^{3} v^{2} - 4 u^{2} v^{3} + 8 u v^{4})$

Step 4

Apply the distributive property.

$\frac{1}{2} (10 u^{3} v^{2}) + \frac{1}{2} (- 4 u^{2} v^{3}) + \frac{1}{2} (8 u v^{4})$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $2$ .

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Step 5.1.1

Factor $2$ out of $10 u^{3} v^{2}$ .

$\frac{1}{2} (2 (5 u^{3} v^{2})) + \frac{1}{2} (- 4 u^{2} v^{3}) + \frac{1}{2} (8 u v^{4})$

Step 5.1.2

Cancel the common factor.

$\frac{1}{2} (2 (5 u^{3} v^{2})) + \frac{1}{2} (- 4 u^{2} v^{3}) + \frac{1}{2} (8 u v^{4})$

Step 5.1.3

Rewrite the expression.

$5 u^{3} v^{2} + \frac{1}{2} (- 4 u^{2} v^{3}) + \frac{1}{2} (8 u v^{4})$

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Factor $2$ out of $- 4 u^{2} v^{3}$ .

$5 u^{3} v^{2} + \frac{1}{2} (2 (- 2 u^{2} v^{3})) + \frac{1}{2} (8 u v^{4})$

Step 5.2.2

Cancel the common factor.

$5 u^{3} v^{2} + \frac{1}{2} (2 (- 2 u^{2} v^{3})) + \frac{1}{2} (8 u v^{4})$

Step 5.2.3

Rewrite the expression.

$5 u^{3} v^{2} - 2 u^{2} v^{3} + \frac{1}{2} (8 u v^{4})$

Step 5.3

Cancel the common factor of $2$ .

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Step 5.3.1

Factor $2$ out of $8 u v^{4}$ .

$5 u^{3} v^{2} - 2 u^{2} v^{3} + \frac{1}{2} (2 (4 u v^{4}))$

Step 5.3.2

Cancel the common factor.

$5 u^{3} v^{2} - 2 u^{2} v^{3} + \frac{1}{2} (2 (4 u v^{4}))$

Step 5.3.3

Rewrite the expression.

$5 u^{3} v^{2} - 2 u^{2} v^{3} + 4 u v^{4}$