Basic Math Examples

$(\frac{3 m}{6 m + 18}) (m^{2} - 7 m - 30)$

Step 1

Factor $6$ out of $6 m + 18$ .

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Step 1.1

Factor $6$ out of $6 m$ .

$\frac{3 m}{6 (m) + 18} (m^{2} - 7 m - 30)$

Step 1.2

Factor $6$ out of $18$ .

$\frac{3 m}{6 m + 6 \cdot 3} (m^{2} - 7 m - 30)$

Step 1.3

Factor $6$ out of $6 m + 6 \cdot 3$ .

$\frac{3 m}{6 (m + 3)} (m^{2} - 7 m - 30)$

Step 2

Cancel the common factor of $3$ and $6$ .

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Step 2.1

Factor $3$ out of $3 m$ .

$\frac{3 (m)}{6 (m + 3)} (m^{2} - 7 m - 30)$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $6 (m + 3)$ .

$\frac{3 (m)}{3 (2 (m + 3))} (m^{2} - 7 m - 30)$

Step 2.2.2

Cancel the common factor.

$\frac{3 m}{3 (2 (m + 3))} (m^{2} - 7 m - 30)$

Step 2.2.3

Rewrite the expression.

$\frac{m}{2 (m + 3)} (m^{2} - 7 m - 30)$

Step 3

Multiply $\frac{m}{2 (m + 3)}$ by $m^{2} - 7 m - 30$ .

$\frac{m (m^{2} - 7 m - 30)}{2 (m + 3)}$

Step 4

Factor $m^{2} - 7 m - 30$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 30$ and whose sum is $- 7$ .

$- 10, 3$

Step 4.2

Write the factored form using these integers.

$\frac{m ((m - 10) (m + 3))}{2 (m + 3)}$

$\frac{m (m - 10) (m + 3)}{2 (m + 3)}$

Step 5

Cancel the common factor of $m + 3$ .

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Step 5.1

Cancel the common factor.

$\frac{m (m - 10) (m + 3)}{2 (m + 3)}$

Step 5.2

Rewrite the expression.

$\frac{m (m - 10)}{2}$