Algebra Examples

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

Step 1

Add $- 8 a^{2}$ and $a^{2}$ .

$(4 a^{3} - 7 a^{2}) {(4 a)}^{- 1}$

Step 2

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

$(4 a^{3} - 7 a^{2}) \frac{1}{4 a}$

Step 3

Multiply $4 a^{3} - 7 a^{2}$ by $\frac{1}{4 a}$ .

$\frac{4 a^{3} - 7 a^{2}}{4 a}$

Step 4

Factor $a^{2}$ out of $4 a^{3} - 7 a^{2}$ .

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Step 4.1

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

$\frac{a^{2} (4 a) - 7 a^{2}}{4 a}$

Step 4.2

Factor $a^{2}$ out of $- 7 a^{2}$ .

$\frac{a^{2} (4 a) + a^{2} \cdot - 7}{4 a}$

Step 4.3

Factor $a^{2}$ out of $a^{2} (4 a) + a^{2} \cdot - 7$ .

$\frac{a^{2} (4 a - 7)}{4 a}$

Step 5

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

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Step 5.1

Factor $a$ out of $a^{2} (4 a - 7)$ .

$\frac{a (a (4 a - 7))}{4 a}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $a$ out of $4 a$ .

$\frac{a (a (4 a - 7))}{a \cdot 4}$

Step 5.2.2

Cancel the common factor.

$\frac{a (a (4 a - 7))}{a \cdot 4}$

Step 5.2.3

Rewrite the expression.

$\frac{a (4 a - 7)}{4}$