Algebra Examples

$\frac{4 x^{10} - 5 x^{9} - 20 x^{4}}{4 x^{2}}$

Step 1

Factor $x^{4}$ out of $4 x^{10} - 5 x^{9} - 20 x^{4}$ .

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Step 1.1

Factor $x^{4}$ out of $4 x^{10}$ .

$\frac{x^{4} (4 x^{6}) - 5 x^{9} - 20 x^{4}}{4 x^{2}}$

Step 1.2

Factor $x^{4}$ out of $- 5 x^{9}$ .

$\frac{x^{4} (4 x^{6}) + x^{4} (- 5 x^{5}) - 20 x^{4}}{4 x^{2}}$

Step 1.3

Factor $x^{4}$ out of $- 20 x^{4}$ .

$\frac{x^{4} (4 x^{6}) + x^{4} (- 5 x^{5}) + x^{4} \cdot - 20}{4 x^{2}}$

Step 1.4

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

$\frac{x^{4} (4 x^{6} - 5 x^{5}) + x^{4} \cdot - 20}{4 x^{2}}$

Step 1.5

Factor $x^{4}$ out of $x^{4} (4 x^{6} - 5 x^{5}) + x^{4} \cdot - 20$ .

$\frac{x^{4} (4 x^{6} - 5 x^{5} - 20)}{4 x^{2}}$

Step 2

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $x^{4} (4 x^{6} - 5 x^{5} - 20)$ .

$\frac{x^{2} (x^{2} (4 x^{6} - 5 x^{5} - 20))}{4 x^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{2}$ out of $4 x^{2}$ .

$\frac{x^{2} (x^{2} (4 x^{6} - 5 x^{5} - 20))}{x^{2} \cdot 4}$

Step 2.2.2

Cancel the common factor.

$\frac{x^{2} (x^{2} (4 x^{6} - 5 x^{5} - 20))}{x^{2} \cdot 4}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{2} (4 x^{6} - 5 x^{5} - 20)}{4}$

Step 3

Apply the distributive property.

$\frac{x^{2} (4 x^{6}) + x^{2} (- 5 x^{5}) + x^{2} \cdot - 20}{4}$

Step 4

Simplify.

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Step 4.1

Rewrite using the commutative property of multiplication.

$\frac{4 x^{2} x^{6} + x^{2} (- 5 x^{5}) + x^{2} \cdot - 20}{4}$

Step 4.2

Rewrite using the commutative property of multiplication.

$\frac{4 x^{2} x^{6} - 5 x^{2} x^{5} + x^{2} \cdot - 20}{4}$

Step 4.3

Move $- 20$ to the left of $x^{2}$ .

$\frac{4 x^{2} x^{6} - 5 x^{2} x^{5} - 20 \cdot x^{2}}{4}$

Step 5

Simplify each term.

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Step 5.1

Multiply $x^{2}$ by $x^{6}$ by adding the exponents.

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Step 5.1.1

Move $x^{6}$ .

$\frac{4 (x^{6} x^{2}) - 5 x^{2} x^{5} - 20 \cdot x^{2}}{4}$

Step 5.1.2

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

$\frac{4 x^{6 + 2} - 5 x^{2} x^{5} - 20 \cdot x^{2}}{4}$

Step 5.1.3

Add $6$ and $2$ .

$\frac{4 x^{8} - 5 x^{2} x^{5} - 20 \cdot x^{2}}{4}$

Step 5.2

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

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Step 5.2.1

Move $x^{5}$ .

$\frac{4 x^{8} - 5 (x^{5} x^{2}) - 20 \cdot x^{2}}{4}$

Step 5.2.2

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

$\frac{4 x^{8} - 5 x^{5 + 2} - 20 \cdot x^{2}}{4}$

Step 5.2.3

Add $5$ and $2$ .

$\frac{4 x^{8} - 5 x^{7} - 20 \cdot x^{2}}{4}$

$\frac{4 x^{8} - 5 x^{7} - 20 x^{2}}{4}$

Step 6

Split the fraction $\frac{4 x^{8} - 5 x^{7} - 20 x^{2}}{4}$ into two fractions.

$\frac{4 x^{8} - 5 x^{7}}{4} + \frac{- 20 x^{2}}{4}$

Step 7

Split the fraction $\frac{4 x^{8} - 5 x^{7}}{4}$ into two fractions.

$\frac{4 x^{8}}{4} + \frac{- 5 x^{7}}{4} + \frac{- 20 x^{2}}{4}$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Cancel the common factor.

$\frac{4 x^{8}}{4} + \frac{- 5 x^{7}}{4} + \frac{- 20 x^{2}}{4}$

Step 8.2

Divide $x^{8}$ by $1$ .

$x^{8} + \frac{- 5 x^{7}}{4} + \frac{- 20 x^{2}}{4}$

Step 9

Move the negative in front of the fraction.

$x^{8} - \frac{5 x^{7}}{4} + \frac{- 20 x^{2}}{4}$

Step 10

Cancel the common factor of $- 20$ and $4$ .

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Step 10.1

Factor $4$ out of $- 20 x^{2}$ .

$x^{8} - \frac{5 x^{7}}{4} + \frac{4 (- 5 x^{2})}{4}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $4$ out of $4$ .

$x^{8} - \frac{5 x^{7}}{4} + \frac{4 (- 5 x^{2})}{4 (1)}$

Step 10.2.2

Cancel the common factor.

$x^{8} - \frac{5 x^{7}}{4} + \frac{4 (- 5 x^{2})}{4 \cdot 1}$

Step 10.2.3

Rewrite the expression.

$x^{8} - \frac{5 x^{7}}{4} + \frac{- 5 x^{2}}{1}$

Step 10.2.4

Divide $- 5 x^{2}$ by $1$ .

$x^{8} - \frac{5 x^{7}}{4} - 5 x^{2}$