Algebra Examples

$\frac{1}{5} p q - \frac{3}{10} p q^{3} - \frac{3}{5} p q^{3} - \frac{7}{10} p q + 3 p q$

Step 1

Remove parentheses.

$\frac{1}{5} \cdot p q - \frac{3}{10} \cdot (p q^{3}) - \frac{3}{5} \cdot (p q^{3}) - \frac{7}{10} \cdot (p q) + 3 p q$

Step 2

Remove parentheses.

$\frac{1}{5} \cdot p q - \frac{3}{10} \cdot p q^{3} - \frac{3}{5} \cdot (p q^{3}) - \frac{7}{10} \cdot (p q) + 3 p q$

Step 3

Remove parentheses.

$\frac{1}{5} \cdot p q - \frac{3}{10} \cdot p q^{3} - \frac{3}{5} \cdot p q^{3} - \frac{7}{10} \cdot (p q) + 3 p q$

Step 4

Remove parentheses.

$\frac{1}{5} \cdot p q - \frac{3}{10} \cdot p q^{3} - \frac{3}{5} \cdot p q^{3} - \frac{7}{10} \cdot p q + 3 p q$

Step 5

Factor $p q$ out of $\frac{1}{5} \cdot p q - \frac{3}{10} \cdot p q^{3} - \frac{3}{5} \cdot p q^{3} - \frac{7}{10} \cdot p q + 3 p q$ .

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Step 5.1

Factor $p q$ out of $\frac{1}{5} \cdot p q$ .

$p q (\frac{1}{5}) - \frac{3}{10} \cdot p q^{3} - \frac{3}{5} \cdot p q^{3} - \frac{7}{10} \cdot p q + 3 p q$

Step 5.2

Factor $p q$ out of $- \frac{3}{10} \cdot p q^{3}$ .

$p q (\frac{1}{5}) + p q (- \frac{3}{10} q^{2}) - \frac{3}{5} \cdot p q^{3} - \frac{7}{10} \cdot p q + 3 p q$

Step 5.3

Factor $p q$ out of $- \frac{3}{5} \cdot p q^{3}$ .

$p q (\frac{1}{5}) + p q (- \frac{3}{10} q^{2}) + p q (- \frac{3}{5} q^{2}) - \frac{7}{10} \cdot p q + 3 p q$

Step 5.4

Factor $p q$ out of $- \frac{7}{10} \cdot p q$ .

$p q (\frac{1}{5}) + p q (- \frac{3}{10} q^{2}) + p q (- \frac{3}{5} q^{2}) + p q (- \frac{7}{10}) + 3 p q$

Step 5.5

Factor $p q$ out of $3 p q$ .

$p q (\frac{1}{5}) + p q (- \frac{3}{10} q^{2}) + p q (- \frac{3}{5} q^{2}) + p q (- \frac{7}{10}) + p q (3)$

Step 5.6

Factor $p q$ out of $p q (\frac{1}{5}) + p q (- \frac{3}{10} q^{2})$ .

$p q (\frac{1}{5} - \frac{3}{10} q^{2}) + p q (- \frac{3}{5} q^{2}) + p q (- \frac{7}{10}) + p q (3)$

Step 5.7

Factor $p q$ out of $p q (\frac{1}{5} - \frac{3}{10} q^{2}) + p q (- \frac{3}{5} q^{2})$ .

$p q (\frac{1}{5} - \frac{3}{10} q^{2} - \frac{3}{5} q^{2}) + p q (- \frac{7}{10}) + p q (3)$

Step 5.8

Factor $p q$ out of $p q (\frac{1}{5} - \frac{3}{10} q^{2} - \frac{3}{5} q^{2}) + p q (- \frac{7}{10})$ .

$p q (\frac{1}{5} - \frac{3}{10} q^{2} - \frac{3}{5} q^{2} - \frac{7}{10}) + p q (3)$

Step 5.9

Factor $p q$ out of $p q (\frac{1}{5} - \frac{3}{10} q^{2} - \frac{3}{5} q^{2} - \frac{7}{10}) + p q (3)$ .

$p q (\frac{1}{5} - \frac{3}{10} q^{2} - \frac{3}{5} q^{2} - \frac{7}{10} + 3)$

Step 6

Combine exponents.

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Step 6.1

Combine $q^{2}$ and $\frac{3}{10}$ .

$p q (\frac{1}{5} - \frac{q^{2} \cdot 3}{10} - \frac{3}{5} q^{2} - \frac{7}{10} + 3)$

Step 6.2

Combine $q^{2}$ and $\frac{3}{5}$ .

$p q (\frac{1}{5} - \frac{q^{2} \cdot 3}{10} - \frac{q^{2} \cdot 3}{5} - \frac{7}{10} + 3)$