Algebra Examples

$2 m (\frac{3}{2} m + 1) + 3 (\frac{5}{3} m - 2)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{3}{2}$ and $m$ .

$2 m (\frac{3 m}{2} + 1) + 3 (\frac{5}{3} m - 2)$

Step 1.2

Apply the distributive property.

$2 m \frac{3 m}{2} + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $2 m$ .

$2 (m) \frac{3 m}{2} + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.3.2

Cancel the common factor.

$2 m \frac{3 m}{2} + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.3.3

Rewrite the expression.

$m (3 m) + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.4

Raise $m$ to the power of $1$ .

$3 (m^{1} m) + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.5

Raise $m$ to the power of $1$ .

$3 (m^{1} m^{1}) + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 m^{1 + 1} + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.7

Add $1$ and $1$ .

$3 m^{2} + 2 m \cdot 1 + 3 (\frac{5}{3} m - 2)$

Step 1.8

Multiply $2$ by $1$ .

$3 m^{2} + 2 m + 3 (\frac{5}{3} m - 2)$

Step 1.9

Combine $\frac{5}{3}$ and $m$ .

$3 m^{2} + 2 m + 3 (\frac{5 m}{3} - 2)$

Step 1.10

Apply the distributive property.

$3 m^{2} + 2 m + 3 \frac{5 m}{3} + 3 \cdot - 2$

Step 1.11

Cancel the common factor of $3$ .

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Step 1.11.1

Cancel the common factor.

$3 m^{2} + 2 m + 3 \frac{5 m}{3} + 3 \cdot - 2$

Step 1.11.2

Rewrite the expression.

$3 m^{2} + 2 m + 5 m + 3 \cdot - 2$

Step 1.12

Multiply $3$ by $- 2$ .

$3 m^{2} + 2 m + 5 m - 6$

Step 2

Add $2 m$ and $5 m$ .

$3 m^{2} + 7 m - 6$