Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

Multiply $2$ by $- 3$ .

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $6 p q$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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

Step 2.4

Multiply $2$ by $2$ .

$- 6 p^{2} + 4 p q - 12 q^{2} \frac{2}{3}$

Step 2.5

Cancel the common factor of $3$ .

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Step 2.5.1

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

$- 6 p^{2} + 4 p q + 3 (- 4 q^{2}) \frac{2}{3}$

Step 2.5.2

Cancel the common factor.

$- 6 p^{2} + 4 p q + 3 (- 4 q^{2}) \frac{2}{3}$

Step 2.5.3

Rewrite the expression.

$- 6 p^{2} + 4 p q - 4 q^{2} \cdot 2$

Step 2.6

Multiply $2$ by $- 4$ .

$- 6 p^{2} + 4 p q - 8 q^{2}$