Basic Math Examples

$(- 5 w^{10} + 10 w^{8} + 5 w^{6}) \div 5 w^{5}$

Step 1

Rewrite the division as a fraction.

$\frac{- 5 w^{10} + 10 w^{8} + 5 w^{6}}{5 w^{5}}$

Step 2

Factor $5 w^{6}$ out of $- 5 w^{10} + 10 w^{8} + 5 w^{6}$ .

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Step 2.1

Factor $5 w^{6}$ out of $- 5 w^{10}$ .

$\frac{5 w^{6} (- w^{4}) + 10 w^{8} + 5 w^{6}}{5 w^{5}}$

Step 2.2

Factor $5 w^{6}$ out of $10 w^{8}$ .

$\frac{5 w^{6} (- w^{4}) + 5 w^{6} (2 w^{2}) + 5 w^{6}}{5 w^{5}}$

Step 2.3

Factor $5 w^{6}$ out of $5 w^{6}$ .

$\frac{5 w^{6} (- w^{4}) + 5 w^{6} (2 w^{2}) + 5 w^{6} (1)}{5 w^{5}}$

Step 2.4

Factor $5 w^{6}$ out of $5 w^{6} (- w^{4}) + 5 w^{6} (2 w^{2})$ .

$\frac{5 w^{6} (- w^{4} + 2 w^{2}) + 5 w^{6} (1)}{5 w^{5}}$

Step 2.5

Factor $5 w^{6}$ out of $5 w^{6} (- w^{4} + 2 w^{2}) + 5 w^{6} (1)$ .

$\frac{5 w^{6} (- w^{4} + 2 w^{2} + 1)}{5 w^{5}}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 w^{6} (- w^{4} + 2 w^{2} + 1)}{5 w^{5}}$

Step 3.2

Rewrite the expression.

$\frac{w^{6} (- w^{4} + 2 w^{2} + 1)}{w^{5}}$

Step 4

Cancel the common factor of $w^{6}$ and $w^{5}$ .

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Step 4.1

Factor $w^{5}$ out of $w^{6} (- w^{4} + 2 w^{2} + 1)$ .

$\frac{w^{5} (w (- w^{4} + 2 w^{2} + 1))}{w^{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{w^{5} (w (- w^{4} + 2 w^{2} + 1))}{w^{5} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{w^{5} (w (- w^{4} + 2 w^{2} + 1))}{w^{5} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{w (- w^{4} + 2 w^{2} + 1)}{1}$

Step 4.2.4

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

$w (- w^{4} + 2 w^{2} + 1)$

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

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

Step 6.2

Rewrite using the commutative property of multiplication.

$- w \cdot w^{4} + 2 w \cdot w^{2} + w \cdot 1$

Step 6.3

Multiply $w$ by $1$ .

$- w \cdot w^{4} + 2 w \cdot w^{2} + w$

Step 7

Simplify each term.

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Step 7.1

Multiply $w$ by $w^{4}$ by adding the exponents.

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Step 7.1.1

Move $w^{4}$ .

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

Step 7.1.2

Multiply $w^{4}$ by $w$ .

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Step 7.1.2.1

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

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

Step 7.1.2.2

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

$- w^{4 + 1} + 2 w \cdot w^{2} + w$

Step 7.1.3

Add $4$ and $1$ .

$- w^{5} + 2 w \cdot w^{2} + w$

Step 7.2

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

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Step 7.2.1

Move $w^{2}$ .

$- w^{5} + 2 (w^{2} w) + w$

Step 7.2.2

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

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Step 7.2.2.1

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

$- w^{5} + 2 (w^{2} w^{1}) + w$

Step 7.2.2.2

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

$- w^{5} + 2 w^{2 + 1} + w$

Step 7.2.3

Add $2$ and $1$ .

$- w^{5} + 2 w^{3} + w$