Algebra Examples

$(6 p^{2} q^{2} - 9 p^{2} q + 12 p q^{2}) \div (- 3 p q)$

Step 1

Rewrite the division as a fraction.

$\frac{6 p^{2} q^{2} - 9 p^{2} q + 12 p q^{2}}{- 3 p q}$

Step 2

Factor $3 p q$ out of $6 p^{2} q^{2} - 9 p^{2} q + 12 p q^{2}$ .

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Step 2.1

Factor $3 p q$ out of $6 p^{2} q^{2}$ .

$\frac{3 p q (2 p q) - 9 p^{2} q + 12 p q^{2}}{- 3 p q}$

Step 2.2

Factor $3 p q$ out of $- 9 p^{2} q$ .

$\frac{3 p q (2 p q) + 3 p q (- 3 p) + 12 p q^{2}}{- 3 p q}$

Step 2.3

Factor $3 p q$ out of $12 p q^{2}$ .

$\frac{3 p q (2 p q) + 3 p q (- 3 p) + 3 p q (4 q)}{- 3 p q}$

Step 2.4

Factor $3 p q$ out of $3 p q (2 p q) + 3 p q (- 3 p)$ .

$\frac{3 p q (2 p q - 3 p) + 3 p q (4 q)}{- 3 p q}$

Step 2.5

Factor $3 p q$ out of $3 p q (2 p q - 3 p) + 3 p q (4 q)$ .

$\frac{3 p q (2 p q - 3 p + 4 q)}{- 3 p q}$

Step 3

Cancel the common factor of $3$ and $- 3$ .

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Step 3.1

Factor $3$ out of $3 p q (2 p q - 3 p + 4 q)$ .

$\frac{3 (p q (2 p q - 3 p + 4 q))}{- 3 p q}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{3 (p q (2 p q - 3 p + 4 q))}{3 (- p q)}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (p q (2 p q - 3 p + 4 q))}{3 (- p q)}$

Step 3.2.3

Rewrite the expression.

$\frac{p q (2 p q - 3 p + 4 q)}{- p q}$

Step 4

Cancel the common factor of $p$ .

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Step 4.1

Cancel the common factor.

$\frac{p q (2 p q - 3 p + 4 q)}{- p q}$

Step 4.2

Rewrite the expression.

$\frac{q (2 p q - 3 p + 4 q)}{- 1 q}$

Step 5

Cancel the common factor of $q$ .

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Step 5.1

Cancel the common factor.

$\frac{q (2 p q - 3 p + 4 q)}{- 1 q}$

Step 5.2

Rewrite the expression.

$\frac{2 p q - 3 p + 4 q}{- 1}$

Step 5.3

Move the negative one from the denominator of $\frac{2 p q - 3 p + 4 q}{- 1}$ .

$- 1 \cdot (2 p q - 3 p + 4 q)$

Step 6

Rewrite $- 1 \cdot (2 p q - 3 p + 4 q)$ as $- (2 p q - 3 p + 4 q)$ .

$- (2 p q - 3 p + 4 q)$

Step 7

Apply the distributive property.

$- (2 p q) - (- 3 p) - (4 q)$

Step 8

Simplify.

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Step 8.1

Multiply $2$ by $- 1$ .

$- 2 (p q) - (- 3 p) - (4 q)$

Step 8.2

Multiply $- 3$ by $- 1$ .

$- 2 (p q) + 3 p - (4 q)$

Step 8.3

Multiply $4$ by $- 1$ .

$- 2 (p q) + 3 p - 4 q$

$- 2 p q + 3 p - 4 q$