Algebra Examples

$(28 d^{3} k^{2} + d^{2} k^{2} - 4 d k^{2}) {(4 d k^{2})}^{- 1}$

Step 1

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

$(28 d^{3} k^{2} + d^{2} k^{2} - 4 d k^{2}) \frac{1}{4 d k^{2}}$

Step 2

Multiply $28 d^{3} k^{2} + d^{2} k^{2} - 4 d k^{2}$ by $\frac{1}{4 d k^{2}}$ .

$\frac{28 d^{3} k^{2} + d^{2} k^{2} - 4 d k^{2}}{4 d k^{2}}$

Step 3

Factor $d k^{2}$ out of $28 d^{3} k^{2} + d^{2} k^{2} - 4 d k^{2}$ .

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Step 3.1

Factor $d k^{2}$ out of $28 d^{3} k^{2}$ .

$\frac{d k^{2} (28 d^{2}) + d^{2} k^{2} - 4 d k^{2}}{4 d k^{2}}$

Step 3.2

Factor $d k^{2}$ out of $d^{2} k^{2}$ .

$\frac{d k^{2} (28 d^{2}) + d k^{2} (d) - 4 d k^{2}}{4 d k^{2}}$

Step 3.3

Factor $d k^{2}$ out of $- 4 d k^{2}$ .

$\frac{d k^{2} (28 d^{2}) + d k^{2} (d) + d k^{2} (- 4)}{4 d k^{2}}$

Step 3.4

Factor $d k^{2}$ out of $d k^{2} (28 d^{2}) + d k^{2} (d)$ .

$\frac{d k^{2} (28 d^{2} + d) + d k^{2} (- 4)}{4 d k^{2}}$

Step 3.5

Factor $d k^{2}$ out of $d k^{2} (28 d^{2} + d) + d k^{2} (- 4)$ .

$\frac{d k^{2} (28 d^{2} + d - 4)}{4 d k^{2}}$

Step 4

Cancel the common factor of $d$ .

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Step 4.1

Cancel the common factor.

$\frac{d k^{2} (28 d^{2} + d - 4)}{4 d k^{2}}$

Step 4.2

Rewrite the expression.

$\frac{k^{2} (28 d^{2} + d - 4)}{4 k^{2}}$

Step 5

Cancel the common factor of $k^{2}$ .

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Step 5.1

Cancel the common factor.

$\frac{k^{2} (28 d^{2} + d - 4)}{4 k^{2}}$

Step 5.2

Rewrite the expression.

$\frac{28 d^{2} + d - 4}{4}$

Step 6

Split the fraction $\frac{28 d^{2} + d - 4}{4}$ into two fractions.

$\frac{28 d^{2} + d}{4} + \frac{- 4}{4}$

Step 7

Split the fraction $\frac{28 d^{2} + d}{4}$ into two fractions.

$\frac{28 d^{2}}{4} + \frac{d}{4} + \frac{- 4}{4}$

Step 8

Cancel the common factor of $28$ and $4$ .

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Step 8.1

Factor $4$ out of $28 d^{2}$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $4$ out of $4$ .

$\frac{4 (7 d^{2})}{4 (1)} + \frac{d}{4} + \frac{- 4}{4}$

Step 8.2.2

Cancel the common factor.

$\frac{4 (7 d^{2})}{4 \cdot 1} + \frac{d}{4} + \frac{- 4}{4}$

Step 8.2.3

Rewrite the expression.

$\frac{7 d^{2}}{1} + \frac{d}{4} + \frac{- 4}{4}$

Step 8.2.4

Divide $7 d^{2}$ by $1$ .

$7 d^{2} + \frac{d}{4} + \frac{- 4}{4}$

Step 9

Divide $- 4$ by $4$ .

$7 d^{2} + \frac{d}{4} - 1$