Basic Math Examples

$K = (\frac{1}{2}) (m) (b^{2}) + (m) (g) (h) - \frac{1}{2} m v^{2} + (m) (g) (h)$

Step 1

Multiply $\frac{1}{2}$ by $m$ .

$K = \frac{1}{2} \cdot ((m) b^{2}) + (m) (g) (h) - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 2

Multiply $\frac{1}{2}$ by $m$ .

$K = \frac{1}{2} \cdot (m b^{2}) + (m) (g) (h) - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 3

Multiply $m$ by $g$ .

$K = \frac{1}{2} \cdot (m b^{2}) + m (g) h - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 4

Multiply $m$ by $g$ .

$K = \frac{1}{2} \cdot (m b^{2}) + m g h - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 5

Remove parentheses.

$K = \frac{1}{2} \cdot (m b^{2}) + m g h - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 6

Multiply $m$ by $g$ .

$K = \frac{1}{2} \cdot (m b^{2}) + m g h - \frac{1}{2} \cdot (m v^{2}) + m (g) h$

Step 7

Multiply $m$ by $g$ .

$K = \frac{1}{2} \cdot (m b^{2}) + m g h - \frac{1}{2} \cdot (m v^{2}) + m g h$

Step 8

Remove parentheses.

$K = (\frac{1}{2}) (m) (b^{2}) + (m) (g) (h) - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 9

Simplify $(\frac{1}{2}) (m) (b^{2}) + (m) (g) (h) - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$ .

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Step 9.1

Simplify each term.

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Step 9.1.1

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

$K = \frac{m}{2} b^{2} + (m) (g) (h) - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 9.1.2

Combine $\frac{m}{2}$ and $b^{2}$ .

$K = \frac{m b^{2}}{2} + (m) (g) (h) - \frac{1}{2} \cdot (m v^{2}) + (m) (g) (h)$

Step 9.1.3

Multiply $- \frac{1}{2} (m v^{2})$ .

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Step 9.1.3.1

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

$K = \frac{m b^{2}}{2} + m g h - \frac{m}{2} v^{2} + (m) (g) (h)$

Step 9.1.3.2

Combine $v^{2}$ and $\frac{m}{2}$ .

$K = \frac{m b^{2}}{2} + m g h - \frac{v^{2} m}{2} + (m) (g) (h)$

$K = \frac{m b^{2}}{2} + m g h - \frac{v^{2} m}{2} + m g h$

Step 9.2

Simplify by adding terms.

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Step 9.2.1

Add $m g h$ and $m g h$ .

$K = \frac{m b^{2}}{2} - \frac{v^{2} m}{2} + 2 m g h$

Step 9.2.2

Simplify the expression.

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Step 9.2.2.1

Reorder $m$ and $b^{2}$ .

$K = \frac{b^{2} m}{2} - \frac{v^{2} m}{2} + 2 m g h$

Step 9.2.2.2

Reorder $v^{2}$ and $m$ .

$K = \frac{b^{2} m}{2} - \frac{m v^{2}}{2} + 2 m g h$

Step 9.2.2.3

Move $m$ .

$K = \frac{b^{2} m}{2} - \frac{m v^{2}}{2} + 2 g h m$

Step 9.2.2.4

Move $- \frac{m v^{2}}{2}$ .

$K = \frac{b^{2} m}{2} + 2 g h m - \frac{m v^{2}}{2}$

Step 9.2.2.5

Reorder $\frac{b^{2} m}{2}$ and $2 g h m$ .

$K = 2 g h m + \frac{b^{2} m}{2} - \frac{m v^{2}}{2}$