Basic Math Examples

$\frac{2 m + 1}{3 m - 6} \cdot \frac{9 m^{2} - 36}{1}$

Step 1

Factor $3$ out of $3 m - 6$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $3 m$ .

$\frac{2 m + 1}{3 (m) - 6} \cdot \frac{9 m^{2} - 36}{1}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{2 m + 1}{3 m + 3 \cdot - 2} \cdot \frac{9 m^{2} - 36}{1}$

Step 1.3

Factor $3$ out of $3 m + 3 \cdot - 2$ .

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{9 m^{2} - 36}{1}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Factor $9$ out of $9 m^{2} - 36$ .

Tap for more steps...

Step 2.1.1

Factor $9$ out of $9 m^{2}$ .

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{9 (m^{2}) - 36}{1}$

Step 2.1.2

Factor $9$ out of $- 36$ .

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{9 m^{2} + 9 \cdot - 4}{1}$

Step 2.1.3

Factor $9$ out of $9 m^{2} + 9 \cdot - 4$ .

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{9 (m^{2} - 4)}{1}$

Step 2.2

Rewrite $4$ as $2^{2}$ .

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{9 (m^{2} - 2^{2})}{1}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 2$ .

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{9 (m + 2) (m - 2)}{1}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $3 (m - 2)$ .

Tap for more steps...

Step 3.1.1

Factor $3 (m - 2)$ out of $9 (m + 2) (m - 2)$ .

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{3 (m - 2) (3 (m + 2))}{1}$

Step 3.1.2

Cancel the common factor.

$\frac{2 m + 1}{3 (m - 2)} \cdot \frac{3 (m - 2) (3 (m + 2))}{1}$

Step 3.1.3

Rewrite the expression.

$(2 m + 1) \cdot (3 (m + 2))$

Step 3.2

Apply the distributive property.

$(2 m + 1) \cdot (3 m + 3 \cdot 2)$

Step 3.3

Multiply $3$ by $2$ .

$(2 m + 1) \cdot (3 m + 6)$

Step 4

Expand $(2 m + 1) (3 m + 6)$ using the FOIL Method.

Tap for more steps...

Step 4.1

Apply the distributive property.

$2 m (3 m + 6) + 1 (3 m + 6)$

Step 4.2

Apply the distributive property.

$2 m (3 m) + 2 m \cdot 6 + 1 (3 m + 6)$

Step 4.3

Apply the distributive property.

$2 m (3 m) + 2 m \cdot 6 + 1 (3 m) + 1 \cdot 6$

Step 5

Simplify and combine like terms.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 m \cdot m + 2 m \cdot 6 + 1 (3 m) + 1 \cdot 6$

Step 5.1.2

Multiply $m$ by $m$ by adding the exponents.

Tap for more steps...

Step 5.1.2.1

Move $m$ .

$2 \cdot 3 (m \cdot m) + 2 m \cdot 6 + 1 (3 m) + 1 \cdot 6$

Step 5.1.2.2

Multiply $m$ by $m$ .

$2 \cdot 3 m^{2} + 2 m \cdot 6 + 1 (3 m) + 1 \cdot 6$

Step 5.1.3

Multiply $2$ by $3$ .

$6 m^{2} + 2 m \cdot 6 + 1 (3 m) + 1 \cdot 6$

Step 5.1.4

Multiply $6$ by $2$ .

$6 m^{2} + 12 m + 1 (3 m) + 1 \cdot 6$

Step 5.1.5

Multiply $3 m$ by $1$ .

$6 m^{2} + 12 m + 3 m + 1 \cdot 6$

Step 5.1.6

Multiply $6$ by $1$ .

$6 m^{2} + 12 m + 3 m + 6$

Step 5.2

Add $12 m$ and $3 m$ .

$6 m^{2} + 15 m + 6$