Algebra Examples

$\frac{1}{2} a b^{3} c - \frac{3}{2} a b^{3} c - a b^{3} c$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{2} (a b^{3} c)$ .

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Step 1.1.1

Combine $a$ and $\frac{1}{2}$ .

$\frac{a}{2} (b^{3} c) - \frac{3}{2} \cdot (a b^{3} c) - a b^{3} c$

Step 1.1.2

Combine $b^{3}$ and $\frac{a}{2}$ .

$\frac{b^{3} a}{2} c - \frac{3}{2} \cdot (a b^{3} c) - a b^{3} c$

Step 1.1.3

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

$\frac{b^{3} a c}{2} - \frac{3}{2} \cdot (a b^{3} c) - a b^{3} c$

Step 1.2

Multiply $- \frac{3}{2} (a b^{3} c)$ .

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Step 1.2.1

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

$\frac{b^{3} a c}{2} - \frac{a \cdot 3}{2} (b^{3} c) - a b^{3} c$

Step 1.2.2

Combine $b^{3}$ and $\frac{a \cdot 3}{2}$ .

$\frac{b^{3} a c}{2} - \frac{b^{3} (a \cdot 3)}{2} c - a b^{3} c$

Step 1.2.3

Combine $c$ and $\frac{b^{3} (a \cdot 3)}{2}$ .

$\frac{b^{3} a c}{2} - \frac{c (b^{3} (a \cdot 3))}{2} - a b^{3} c$

Step 1.3

Move $3$ to the left of $c b^{3} a$ .

$\frac{b^{3} a c}{2} - \frac{3 c b^{3} a}{2} - a b^{3} c$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- a b^{3} c + \frac{b^{3} a c - 3 c b^{3} a}{2}$

Step 2.2

Move $b^{3}$ .

$- a b^{3} c + \frac{a b^{3} c - 3 a b^{3} c}{2}$

Step 2.3

Subtract $3 a b^{3} c$ from $a b^{3} c$ .

$- a b^{3} c + \frac{- 2 a b^{3} c}{2}$

Step 2.4

Cancel the common factor of $- 2$ and $2$ .

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Step 2.4.1

Factor $2$ out of $- 2 a b^{3} c$ .

$- a b^{3} c + \frac{2 (- a b^{3} c)}{2}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $2$ .

$- a b^{3} c + \frac{2 (- a b^{3} c)}{2 (1)}$

Step 2.4.2.2

Cancel the common factor.

$- a b^{3} c + \frac{2 (- a b^{3} c)}{2 \cdot 1}$

Step 2.4.2.3

Rewrite the expression.

$- a b^{3} c + \frac{- a b^{3} c}{1}$

Step 2.4.2.4

Divide $- a b^{3} c$ by $1$ .

$- a b^{3} c - a b^{3} c$

Step 2.5

Subtract $a b^{3} c$ from $- a b^{3} c$ .

$- 2 a b^{3} c$