Simplify 3/2u^2v^4-2 1/2u^3v^5+1/2u^4v^2

$\frac{3}{2} u^{2} v^{4} - 2 \frac{1}{2} u^{3} v^{5} + \frac{1}{2} u^{4} v^{2}$

Step 1

Convert $2 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{3}{2} \cdot (u^{2} v^{4}) - (2 + \frac{1}{2}) u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Add $2$ and $\frac{1}{2}$ .

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

$\frac{3}{2} \cdot (u^{2} v^{4}) - (2 \cdot \frac{2}{2} + \frac{1}{2}) u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

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

$\frac{3}{2} \cdot (u^{2} v^{4}) - (\frac{2 \cdot 2}{2} + \frac{1}{2}) u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Combine the numerators over the common denominator.

$\frac{3}{2} \cdot (u^{2} v^{4}) - \frac{2 \cdot 2 + 1}{2} u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{3}{2} \cdot (u^{2} v^{4}) - \frac{4 + 1}{2} u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Add $4$ and $1$ .

$\frac{3}{2} \cdot (u^{2} v^{4}) - \frac{5}{2} u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Step 2

Simplify each term.

Multiply $\frac{3}{2} (u^{2} v^{4})$ .

Combine $u^{2}$ and $\frac{3}{2}$ .

$\frac{u^{2} \cdot 3}{2} v^{4} - \frac{5}{2} u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Combine $\frac{u^{2} \cdot 3}{2}$ and $v^{4}$ .

$\frac{u^{2} \cdot 3 v^{4}}{2} - \frac{5}{2} u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Move $3$ to the left of $u^{2}$ .

$\frac{3 \cdot u^{2} v^{4}}{2} - \frac{5}{2} u^{3} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

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

$\frac{3 u^{2} v^{4}}{2} - \frac{u^{3} \cdot 5}{2} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

Move $5$ to the left of $u^{3}$ .

$\frac{3 u^{2} v^{4}}{2} - \frac{5 \cdot u^{3}}{2} v^{5} + \frac{1}{2} \cdot (u^{4} v^{2})$

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

$\frac{3 u^{2} v^{4}}{2} - \frac{v^{5} (5 u^{3})}{2} + \frac{1}{2} \cdot (u^{4} v^{2})$

Move $5$ to the left of $v^{5}$ .

$\frac{3 u^{2} v^{4}}{2} - \frac{5 \cdot v^{5} u^{3}}{2} + \frac{1}{2} \cdot (u^{4} v^{2})$

Multiply $\frac{1}{2} (u^{4} v^{2})$ .

Combine $u^{4}$ and $\frac{1}{2}$ .

$\frac{3 u^{2} v^{4}}{2} - \frac{5 v^{5} u^{3}}{2} + \frac{u^{4}}{2} v^{2}$

Combine $\frac{u^{4}}{2}$ and $v^{2}$ .

$\frac{3 u^{2} v^{4}}{2} - \frac{5 v^{5} u^{3}}{2} + \frac{u^{4} v^{2}}{2}$

Step 3

Simplify terms.

Combine the numerators over the common denominator.

$\frac{3 u^{2} v^{4} - 5 v^{5} u^{3}}{2} + \frac{u^{4} v^{2}}{2}$

Combine the numerators over the common denominator.

$\frac{3 u^{2} v^{4} - 5 v^{5} u^{3} + u^{4} v^{2}}{2}$

Factor $u^{2} v^{2}$ out of $3 u^{2} v^{4} - 5 v^{5} u^{3} + u^{4} v^{2}$ .

Factor $u^{2} v^{2}$ out of $3 u^{2} v^{4}$ .

$\frac{u^{2} v^{2} (3 v^{2}) - 5 v^{5} u^{3} + u^{4} v^{2}}{2}$

Factor $u^{2} v^{2}$ out of $- 5 v^{5} u^{3}$ .

$\frac{u^{2} v^{2} (3 v^{2}) + u^{2} v^{2} (- 5 v^{3} u) + u^{4} v^{2}}{2}$

Factor $u^{2} v^{2}$ out of $u^{4} v^{2}$ .

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

Factor $u^{2} v^{2}$ out of $u^{2} v^{2} (3 v^{2}) + u^{2} v^{2} (- 5 v^{3} u)$ .

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

Factor $u^{2} v^{2}$ out of $u^{2} v^{2} (3 v^{2} - 5 v^{3} u) + u^{2} v^{2} (u^{2})$ .

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

Simplify 3/2u^2v^4-2 1/2u^3v^5+1/2u^4v^2

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