Simplify (-5w^10+10w^8+5w^6)÷5w^5

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

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

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

Factor

$5 w^{6}$ out of

$- 5 w^{10}$ .

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

Factor

$5 w^{6}$ out of

$10 w^{8}$ .

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

Factor

$5 w^{6}$ out of

$5 w^{6}$ .

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

Factor

$5 w^{6}$ out of

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

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

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

$5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of

$w^{6}$ and

$w^{5}$ .

Factor

$w^{5}$ out of

$w^{6} (- w^{4} + 2 w^{2} + 1)$ .

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

Cancel the common factors.

Multiply by

$1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply

$w$ by

$1$ .

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

Step 7

Simplify each term.

Multiply

$w$ by

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

Move

$w^{4}$ .

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

Multiply

$w^{4}$ by

$w$ .

Raise

$w$ to the power of

$1$ .

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

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add

$4$ and

$1$ .

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

Multiply

$w$ by

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

Move

$w^{2}$ .

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

Multiply

$w^{2}$ by

$w$ .

Raise

$w$ to the power of

$1$ .

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

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add

$2$ and

$1$ .

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

Simplify (-5w^10+10w^8+5w^6)÷5w^5

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