Algebra Examples

$\frac{2}{5} c d^{2} - \frac{1}{3} c d^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{2}{5} (c d^{2})$ .

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Step 1.1.1

Combine $c$ and $\frac{2}{5}$ .

$\frac{c \cdot 2}{5} d^{2} - \frac{1}{3} \cdot (c d^{2})$

Step 1.1.2

Combine $\frac{c \cdot 2}{5}$ and $d^{2}$ .

$\frac{c \cdot 2 d^{2}}{5} - \frac{1}{3} \cdot (c d^{2})$

Step 1.2

Move $2$ to the left of $c$ .

$\frac{2 \cdot c d^{2}}{5} - \frac{1}{3} \cdot (c d^{2})$

Step 1.3

Multiply $- \frac{1}{3} (c d^{2})$ .

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Step 1.3.1

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

$\frac{2 c d^{2}}{5} - \frac{c}{3} d^{2}$

Step 1.3.2

Combine $d^{2}$ and $\frac{c}{3}$ .

$\frac{2 c d^{2}}{5} - \frac{d^{2} c}{3}$

Step 2

Combine $\frac{2 c d^{2}}{5}$ and $- \frac{d^{2} c}{3}$ using a common denominator.

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Step 2.1

Reorder $d^{2}$ and $c$ .

$\frac{2 c d^{2}}{5} - \frac{c d^{2}}{3}$

Step 2.2

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

$\frac{2 c d^{2}}{5} \cdot \frac{3}{3} - \frac{c d^{2}}{3}$

Step 2.3

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

$\frac{2 c d^{2}}{5} \cdot \frac{3}{3} - \frac{c d^{2}}{3} \cdot \frac{5}{5}$

Step 2.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

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

$\frac{2 c d^{2} \cdot 3}{5 \cdot 3} - \frac{c d^{2}}{3} \cdot \frac{5}{5}$

Step 2.4.2

Multiply $5$ by $3$ .

$\frac{2 c d^{2} \cdot 3}{15} - \frac{c d^{2}}{3} \cdot \frac{5}{5}$

Step 2.4.3

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

$\frac{2 c d^{2} \cdot 3}{15} - \frac{c d^{2} \cdot 5}{3 \cdot 5}$

Step 2.4.4

Multiply $3$ by $5$ .

$\frac{2 c d^{2} \cdot 3}{15} - \frac{c d^{2} \cdot 5}{15}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{2 c d^{2} \cdot 3 - c d^{2} \cdot 5}{15}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $c d^{2}$ out of $2 c d^{2} \cdot 3 - c d^{2} \cdot 5$ .

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Step 3.1.1

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

$\frac{c d^{2} (2 \cdot 3) - c d^{2} \cdot 5}{15}$

Step 3.1.2

Factor $c d^{2}$ out of $- c d^{2} \cdot 5$ .

$\frac{c d^{2} (2 \cdot 3) + c d^{2} (- 1 \cdot 5)}{15}$

Step 3.1.3

Factor $c d^{2}$ out of $c d^{2} (2 \cdot 3) + c d^{2} (- 1 \cdot 5)$ .

$\frac{c d^{2} (2 \cdot 3 - 1 \cdot 5)}{15}$

Step 3.2

Combine exponents.

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Step 3.2.1

Multiply $2$ by $3$ .

$\frac{c d^{2} (6 - 1 \cdot 5)}{15}$

Step 3.2.2

Multiply $- 1$ by $5$ .

$\frac{c d^{2} (6 - 5)}{15}$

Step 3.3

Subtract $5$ from $6$ .

$\frac{c d^{2} \cdot 1}{15}$

Step 3.4

Multiply $c$ by $1$ .

$\frac{c d^{2}}{15}$