Algebra Examples

$(4 a^{3} - 8 a^{2} + a) {(4 a)}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(4 a^{3} - 8 a^{2} + a) \frac{1}{4 a}$

Step 2

Multiply $4 a^{3} - 8 a^{2} + a$ by $\frac{1}{4 a}$ .

$\frac{4 a^{3} - 8 a^{2} + a}{4 a}$

Step 3

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

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Step 3.1

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

$\frac{a (4 a^{2}) - 8 a^{2} + a}{4 a}$

Step 3.2

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

$\frac{a (4 a^{2}) + a (- 8 a) + a}{4 a}$

Step 3.3

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

$\frac{a (4 a^{2}) + a (- 8 a) + a^{1}}{4 a}$

Step 3.4

Factor $a$ out of $a^{1}$ .

$\frac{a (4 a^{2}) + a (- 8 a) + a \cdot 1}{4 a}$

Step 3.5

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

$\frac{a (4 a^{2} - 8 a) + a \cdot 1}{4 a}$

Step 3.6

Factor $a$ out of $a (4 a^{2} - 8 a) + a \cdot 1$ .

$\frac{a (4 a^{2} - 8 a + 1)}{4 a}$

Step 4

Cancel the common factor of $a$ .

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Step 4.1

Cancel the common factor.

$\frac{a (4 a^{2} - 8 a + 1)}{4 a}$

Step 4.2

Rewrite the expression.

$\frac{4 a^{2} - 8 a + 1}{4}$