Basic Math Examples

$3 s \sqrt{s t^{3}} - s \sqrt{s^{3} t}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $s t^{3}$ as $t^{2} (s t)$ .

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Step 1.1.1

Factor out $t^{2}$ .

$3 s \sqrt{s (t^{2} t)} - s \sqrt{s^{3} t}$

Step 1.1.2

Reorder $s$ and $t^{2}$ .

$3 s \sqrt{t^{2} s t} - s \sqrt{s^{3} t}$

Step 1.1.3

Add parentheses.

$3 s \sqrt{t^{2} (s t)} - s \sqrt{s^{3} t}$

$3 s \sqrt{t^{2} (s t)} - s \sqrt{s^{3} t}$

Step 1.2

Pull terms out from under the radical.

$3 s (t \sqrt{s t}) - s \sqrt{s^{3} t}$

Step 1.3

Rewrite $s^{3} t$ as $s^{2} (s t)$ .

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Step 1.3.1

Factor out $s^{2}$ .

$3 s (t \sqrt{s t}) - s \sqrt{s^{2} s t}$

Step 1.3.2

Add parentheses.

$3 s (t \sqrt{s t}) - s \sqrt{s^{2} (s t)}$

$3 s (t \sqrt{s t}) - s \sqrt{s^{2} (s t)}$

Step 1.4

Pull terms out from under the radical.

$3 s (t \sqrt{s t}) - s (s \sqrt{s t})$

Step 1.5

Multiply $s$ by $s$ by adding the exponents.

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Step 1.5.1

Move $s$ .

$3 s (t \sqrt{s t}) - (s \cdot s) \sqrt{s t}$

Step 1.5.2

Multiply $s$ by $s$ .

$3 s (t \sqrt{s t}) - s^{2} \sqrt{s t}$

$3 s (t \sqrt{s t}) - s^{2} \sqrt{s t}$

$3 s (t \sqrt{s t}) - s^{2} \sqrt{s t}$

Step 2

Reorder factors in $3 s (t \sqrt{s t}) - s^{2} \sqrt{s t}$ .

$3 s t \sqrt{s t} - s^{2} \sqrt{s t}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$