Algebra Examples

$\frac{3 p^{6} Q + 14 p^{3} Q - 4 p^{3} Q^{2}}{- 7 P^{3} Q}$

Step 1

Factor $p^{3} Q$ out of $3 p^{6} Q + 14 p^{3} Q - 4 p^{3} Q^{2}$ .

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Step 1.1

Factor $p^{3} Q$ out of $3 p^{6} Q$ .

$\frac{p^{3} Q (3 p^{3}) + 14 p^{3} Q - 4 p^{3} Q^{2}}{- 7 P^{3} Q}$

Step 1.2

Factor $p^{3} Q$ out of $14 p^{3} Q$ .

$\frac{p^{3} Q (3 p^{3}) + p^{3} Q (14) - 4 p^{3} Q^{2}}{- 7 P^{3} Q}$

Step 1.3

Factor $p^{3} Q$ out of $- 4 p^{3} Q^{2}$ .

$\frac{p^{3} Q (3 p^{3}) + p^{3} Q (14) + p^{3} Q (- 4 Q)}{- 7 P^{3} Q}$

Step 1.4

Factor $p^{3} Q$ out of $p^{3} Q (3 p^{3}) + p^{3} Q (14)$ .

$\frac{p^{3} Q (3 p^{3} + 14) + p^{3} Q (- 4 Q)}{- 7 P^{3} Q}$

Step 1.5

Factor $p^{3} Q$ out of $p^{3} Q (3 p^{3} + 14) + p^{3} Q (- 4 Q)$ .

$\frac{p^{3} Q (3 p^{3} + 14 - 4 Q)}{- 7 P^{3} Q}$

Step 2

Cancel the common factor of $Q$ .

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Step 2.1

Cancel the common factor.

$\frac{p^{3} Q (3 p^{3} + 14 - 4 Q)}{- 7 P^{3} Q}$

Step 2.2

Rewrite the expression.

$\frac{p^{3} (3 p^{3} + 14 - 4 Q)}{- 7 P^{3}}$

Step 3

Move the negative in front of the fraction.

$- \frac{p^{3} (3 p^{3} + 14 - 4 Q)}{7 P^{3}}$

Step 4

Apply the distributive property.

$- \frac{p^{3} (3 p^{3}) + p^{3} \cdot 14 + p^{3} (- 4 Q)}{7 P^{3}}$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$- \frac{3 p^{3} p^{3} + p^{3} \cdot 14 + p^{3} (- 4 Q)}{7 P^{3}}$

Step 5.2

Move $14$ to the left of $p^{3}$ .

$- \frac{3 p^{3} p^{3} + 14 \cdot p^{3} + p^{3} (- 4 Q)}{7 P^{3}}$

Step 5.3

Rewrite using the commutative property of multiplication.

$- \frac{3 p^{3} p^{3} + 14 \cdot p^{3} - 4 p^{3} Q}{7 P^{3}}$

Step 6

Multiply $p^{3}$ by $p^{3}$ by adding the exponents.

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Step 6.1

Move $p^{3}$ .

$- \frac{3 (p^{3} p^{3}) + 14 \cdot p^{3} - 4 p^{3} Q}{7 P^{3}}$

Step 6.2

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

$- \frac{3 p^{3 + 3} + 14 \cdot p^{3} - 4 p^{3} Q}{7 P^{3}}$

Step 6.3

Add $3$ and $3$ .

$- \frac{3 p^{6} + 14 \cdot p^{3} - 4 p^{3} Q}{7 P^{3}}$

$- \frac{3 p^{6} + 14 p^{3} - 4 p^{3} Q}{7 P^{3}}$

Step 7

Split the fraction $\frac{3 p^{6} + 14 p^{3} - 4 p^{3} Q}{7 P^{3}}$ into two fractions.

$- (\frac{3 p^{6} + 14 p^{3}}{7 P^{3}} + \frac{- 4 p^{3} Q}{7 P^{3}})$

Step 8

Split the fraction $\frac{3 p^{6} + 14 p^{3}}{7 P^{3}}$ into two fractions.

$- (\frac{3 p^{6}}{7 P^{3}} + \frac{14 p^{3}}{7 P^{3}} + \frac{- 4 p^{3} Q}{7 P^{3}})$

Step 9

Cancel the common factor of $14$ and $7$ .

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Step 9.1

Factor $7$ out of $14 p^{3}$ .

$- (\frac{3 p^{6}}{7 P^{3}} + \frac{7 (2 p^{3})}{7 P^{3}} + \frac{- 4 p^{3} Q}{7 P^{3}})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $7$ out of $7 P^{3}$ .

$- (\frac{3 p^{6}}{7 P^{3}} + \frac{7 (2 p^{3})}{7 (P^{3})} + \frac{- 4 p^{3} Q}{7 P^{3}})$

Step 9.2.2

Cancel the common factor.

$- (\frac{3 p^{6}}{7 P^{3}} + \frac{7 (2 p^{3})}{7 P^{3}} + \frac{- 4 p^{3} Q}{7 P^{3}})$

Step 9.2.3

Rewrite the expression.

$- (\frac{3 p^{6}}{7 P^{3}} + \frac{2 p^{3}}{P^{3}} + \frac{- 4 p^{3} Q}{7 P^{3}})$

Step 10

Move the negative in front of the fraction.

$- (\frac{3 p^{6}}{7 P^{3}} + \frac{2 p^{3}}{P^{3}} - \frac{4 p^{3} Q}{7 P^{3}})$