Algebra Examples

$\frac{16 a^{4} - 40 a^{2} + 24 a}{12 a^{3}}$

Step 1

Factor $8 a$ out of $16 a^{4} - 40 a^{2} + 24 a$ .

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Step 1.1

Factor $8 a$ out of $16 a^{4}$ .

$\frac{8 a (2 a^{3}) - 40 a^{2} + 24 a}{12 a^{3}}$

Step 1.2

Factor $8 a$ out of $- 40 a^{2}$ .

$\frac{8 a (2 a^{3}) + 8 a (- 5 a) + 24 a}{12 a^{3}}$

Step 1.3

Factor $8 a$ out of $24 a$ .

$\frac{8 a (2 a^{3}) + 8 a (- 5 a) + 8 a (3)}{12 a^{3}}$

Step 1.4

Factor $8 a$ out of $8 a (2 a^{3}) + 8 a (- 5 a)$ .

$\frac{8 a (2 a^{3} - 5 a) + 8 a (3)}{12 a^{3}}$

Step 1.5

Factor $8 a$ out of $8 a (2 a^{3} - 5 a) + 8 a (3)$ .

$\frac{8 a (2 a^{3} - 5 a + 3)}{12 a^{3}}$

Step 2

Cancel the common factor of $8$ and $12$ .

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Step 2.1

Factor $4$ out of $8 a (2 a^{3} - 5 a + 3)$ .

$\frac{4 (2 a (2 a^{3} - 5 a + 3))}{12 a^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $12 a^{3}$ .

$\frac{4 (2 a (2 a^{3} - 5 a + 3))}{4 (3 a^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (2 a (2 a^{3} - 5 a + 3))}{4 (3 a^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{2 a (2 a^{3} - 5 a + 3)}{3 a^{3}}$

Step 3

Cancel the common factor of $a$ and $a^{3}$ .

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Step 3.1

Factor $a$ out of $2 a (2 a^{3} - 5 a + 3)$ .

$\frac{a (2 (2 a^{3} - 5 a + 3))}{3 a^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $3 a^{3}$ .

$\frac{a (2 (2 a^{3} - 5 a + 3))}{a (3 a^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{a (2 (2 a^{3} - 5 a + 3))}{a (3 a^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 (2 a^{3} - 5 a + 3)}{3 a^{2}}$

Step 4

Apply the distributive property.

$\frac{2 (2 a^{3}) + 2 (- 5 a) + 2 \cdot 3}{3 a^{2}}$

Step 5

Simplify.

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Step 5.1

Multiply $2$ by $2$ .

$\frac{4 a^{3} + 2 (- 5 a) + 2 \cdot 3}{3 a^{2}}$

Step 5.2

Multiply $- 5$ by $2$ .

$\frac{4 a^{3} - 10 a + 2 \cdot 3}{3 a^{2}}$

Step 5.3

Multiply $2$ by $3$ .

$\frac{4 a^{3} - 10 a + 6}{3 a^{2}}$

Step 6

Split the fraction $\frac{4 a^{3} - 10 a + 6}{3 a^{2}}$ into two fractions.

$\frac{4 a^{3} - 10 a}{3 a^{2}} + \frac{6}{3 a^{2}}$

Step 7

Split the fraction $\frac{4 a^{3} - 10 a}{3 a^{2}}$ into two fractions.

$\frac{4 a^{3}}{3 a^{2}} + \frac{- 10 a}{3 a^{2}} + \frac{6}{3 a^{2}}$

Step 8

Cancel the common factor of $a^{3}$ and $a^{2}$ .

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Step 8.1

Factor $a^{2}$ out of $4 a^{3}$ .

$\frac{a^{2} (4 a)}{3 a^{2}} + \frac{- 10 a}{3 a^{2}} + \frac{6}{3 a^{2}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $a^{2}$ out of $3 a^{2}$ .

$\frac{a^{2} (4 a)}{a^{2} \cdot 3} + \frac{- 10 a}{3 a^{2}} + \frac{6}{3 a^{2}}$

Step 8.2.2

Cancel the common factor.

$\frac{a^{2} (4 a)}{a^{2} \cdot 3} + \frac{- 10 a}{3 a^{2}} + \frac{6}{3 a^{2}}$

Step 8.2.3

Rewrite the expression.

$\frac{4 a}{3} + \frac{- 10 a}{3 a^{2}} + \frac{6}{3 a^{2}}$

Step 9

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

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Step 9.1

Factor $a$ out of $- 10 a$ .

$\frac{4 a}{3} + \frac{a \cdot - 10}{3 a^{2}} + \frac{6}{3 a^{2}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $a$ out of $3 a^{2}$ .

$\frac{4 a}{3} + \frac{a \cdot - 10}{a (3 a)} + \frac{6}{3 a^{2}}$

Step 9.2.2

Cancel the common factor.

$\frac{4 a}{3} + \frac{a \cdot - 10}{a (3 a)} + \frac{6}{3 a^{2}}$

Step 9.2.3

Rewrite the expression.

$\frac{4 a}{3} + \frac{- 10}{3 a} + \frac{6}{3 a^{2}}$

Step 10

Move the negative in front of the fraction.

$\frac{4 a}{3} - \frac{10}{3 a} + \frac{6}{3 a^{2}}$

Step 11

Cancel the common factor of $6$ and $3$ .

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Step 11.1

Factor $3$ out of $6$ .

$\frac{4 a}{3} - \frac{10}{3 a} + \frac{3 \cdot 2}{3 a^{2}}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $3$ out of $3 a^{2}$ .

$\frac{4 a}{3} - \frac{10}{3 a} + \frac{3 \cdot 2}{3 (a^{2})}$

Step 11.2.2

Cancel the common factor.

$\frac{4 a}{3} - \frac{10}{3 a} + \frac{3 \cdot 2}{3 a^{2}}$

Step 11.2.3

Rewrite the expression.

$\frac{4 a}{3} - \frac{10}{3 a} + \frac{2}{a^{2}}$