Algebra Examples

$\frac{3}{5} m^{2} - 2 m n + \frac{1}{10} m^{2} - \frac{1}{3} m n + 2 m n - 2 m^{2}$

Step 1

Combine the opposite terms in $\frac{3}{5} m^{2} - 2 m n + \frac{1}{10} m^{2} - \frac{1}{3} \cdot (m n) + 2 m n - 2 m^{2}$ .

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Step 1.1

Add $- 2 m n$ and $2 m n$ .

$\frac{3}{5} m^{2} + \frac{1}{10} m^{2} - \frac{1}{3} \cdot (m n) + 0 - 2 m^{2}$

Step 1.2

Add $\frac{3}{5} m^{2} + \frac{1}{10} m^{2} - \frac{1}{3} \cdot (m n)$ and $0$ .

$\frac{3}{5} m^{2} + \frac{1}{10} m^{2} - \frac{1}{3} \cdot (m n) - 2 m^{2}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{3}{5}$ and $m^{2}$ .

$\frac{3 m^{2}}{5} + \frac{1}{10} m^{2} - \frac{1}{3} \cdot (m n) - 2 m^{2}$

Step 2.2

Combine $\frac{1}{10}$ and $m^{2}$ .

$\frac{3 m^{2}}{5} + \frac{m^{2}}{10} - \frac{1}{3} \cdot (m n) - 2 m^{2}$

Step 2.3

Multiply $- \frac{1}{3} (m n)$ .

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Step 2.3.1

Combine $m$ and $\frac{1}{3}$ .

$\frac{3 m^{2}}{5} + \frac{m^{2}}{10} - \frac{m}{3} n - 2 m^{2}$

Step 2.3.2

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

$\frac{3 m^{2}}{5} + \frac{m^{2}}{10} - \frac{n m}{3} - 2 m^{2}$

Step 3

To write $\frac{3 m^{2}}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 m^{2}}{5} \cdot \frac{2}{2} + \frac{m^{2}}{10} - \frac{n m}{3} - 2 m^{2}$

Step 4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3 m^{2}}{5}$ by $\frac{2}{2}$ .

$\frac{3 m^{2} \cdot 2}{5 \cdot 2} + \frac{m^{2}}{10} - \frac{n m}{3} - 2 m^{2}$

Step 4.2

Multiply $5$ by $2$ .

$\frac{3 m^{2} \cdot 2}{10} + \frac{m^{2}}{10} - \frac{n m}{3} - 2 m^{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 m^{2} \cdot 2 + m^{2}}{10} - \frac{n m}{3} - 2 m^{2}$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Factor $m^{2}$ out of $3 m^{2} \cdot 2 + m^{2}$ .

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Step 6.1.1.1

Factor $m^{2}$ out of $3 m^{2} \cdot 2$ .

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

Step 6.1.1.2

Multiply by $1$ .

$\frac{m^{2} (3 \cdot 2) + m^{2} \cdot 1}{10} - \frac{n m}{3} - 2 m^{2}$

Step 6.1.1.3

Factor $m^{2}$ out of $m^{2} (3 \cdot 2) + m^{2} \cdot 1$ .

$\frac{m^{2} (3 \cdot 2 + 1)}{10} - \frac{n m}{3} - 2 m^{2}$

Step 6.1.2

Multiply $3$ by $2$ .

$\frac{m^{2} (6 + 1)}{10} - \frac{n m}{3} - 2 m^{2}$

Step 6.1.3

Add $6$ and $1$ .

$\frac{m^{2} \cdot 7}{10} - \frac{n m}{3} - 2 m^{2}$

Step 6.2

Move $7$ to the left of $m^{2}$ .

$\frac{7 m^{2}}{10} - \frac{n m}{3} - 2 m^{2}$

Step 7

To write $- 2 m^{2}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- \frac{n m}{3} + \frac{7 m^{2}}{10} - 2 m^{2} \cdot \frac{10}{10}$

Step 8

Simplify terms.

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Step 8.1

Combine $- 2 m^{2}$ and $\frac{10}{10}$ .

$- \frac{n m}{3} + \frac{7 m^{2}}{10} + \frac{- 2 m^{2} \cdot 10}{10}$

Step 8.2

Combine the numerators over the common denominator.

$- \frac{n m}{3} + \frac{7 m^{2} - 2 m^{2} \cdot 10}{10}$

Step 9

Simplify each term.

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Step 9.1

Simplify the numerator.

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Step 9.1.1

Factor $m^{2}$ out of $7 m^{2} - 2 m^{2} \cdot 10$ .

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Step 9.1.1.1

Factor $m^{2}$ out of $7 m^{2}$ .

$- \frac{n m}{3} + \frac{m^{2} \cdot 7 - 2 m^{2} \cdot 10}{10}$

Step 9.1.1.2

Factor $m^{2}$ out of $- 2 m^{2} \cdot 10$ .

$- \frac{n m}{3} + \frac{m^{2} \cdot 7 + m^{2} (- 2 \cdot 10)}{10}$

Step 9.1.1.3

Factor $m^{2}$ out of $m^{2} \cdot 7 + m^{2} (- 2 \cdot 10)$ .

$- \frac{n m}{3} + \frac{m^{2} (7 - 2 \cdot 10)}{10}$

Step 9.1.2

Multiply $- 2$ by $10$ .

$- \frac{n m}{3} + \frac{m^{2} (7 - 20)}{10}$

Step 9.1.3

Subtract $20$ from $7$ .

$- \frac{n m}{3} + \frac{m^{2} \cdot - 13}{10}$

Step 9.2

Move $- 13$ to the left of $m^{2}$ .

$- \frac{n m}{3} + \frac{- 13 \cdot m^{2}}{10}$

Step 9.3

Move the negative in front of the fraction.

$- \frac{n m}{3} - \frac{13 m^{2}}{10}$