Basic Math Examples

$\frac{2 s t^{3} - 8 s^{3} t}{4 s^{2} + 2 s t}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $2 s t$ out of $2 s t^{3} - 8 s^{3} t$ .

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Step 1.1.1

Factor $2 s t$ out of $2 s t^{3}$ .

$\frac{2 s t (t^{2}) - 8 s^{3} t}{4 s^{2} + 2 s t}$

Step 1.1.2

Factor $2 s t$ out of $- 8 s^{3} t$ .

$\frac{2 s t (t^{2}) + 2 s t (- 4 s^{2})}{4 s^{2} + 2 s t}$

Step 1.1.3

Factor $2 s t$ out of $2 s t (t^{2}) + 2 s t (- 4 s^{2})$ .

$\frac{2 s t (t^{2} - 4 s^{2})}{4 s^{2} + 2 s t}$

Step 1.2

Rewrite $4 s^{2}$ as ${(2 s)}^{2}$ .

$\frac{2 s t (t^{2} - {(2 s)}^{2})}{4 s^{2} + 2 s t}$

Step 1.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = t$ and $b = 2 s$ .

$\frac{2 s t ((t + 2 s) (t - (2 s)))}{4 s^{2} + 2 s t}$

Step 1.4

Multiply $2$ by $- 1$ .

$\frac{2 s t (t + 2 s) (t - 2 s)}{4 s^{2} + 2 s t}$

Step 2

Simplify terms.

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Step 2.1

Factor $2 s$ out of $4 s^{2} + 2 s t$ .

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Step 2.1.1

Factor $2 s$ out of $4 s^{2}$ .

$\frac{2 s t (t + 2 s) (t - 2 s)}{2 s (2 s) + 2 s t}$

Step 2.1.2

Factor $2 s$ out of $2 s t$ .

$\frac{2 s t (t + 2 s) (t - 2 s)}{2 s (2 s) + 2 s (t)}$

Step 2.1.3

Factor $2 s$ out of $2 s (2 s) + 2 s (t)$ .

$\frac{2 s t (t + 2 s) (t - 2 s)}{2 s (2 s + t)}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Cancel the common factor.

$\frac{2 s t (t + 2 s) (t - 2 s)}{2 s (2 s + t)}$

Step 2.2.2

Rewrite the expression.

$\frac{(s t (t + 2 s)) (t - 2 s)}{s (2 s + t)}$

Step 2.3

Cancel the common factor of $s$ .

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Step 2.3.1

Cancel the common factor.

$\frac{s t (t + 2 s) (t - 2 s)}{s (2 s + t)}$

Step 2.3.2

Rewrite the expression.

$\frac{(t (t + 2 s)) (t - 2 s)}{2 s + t}$

Step 2.4

Cancel the common factor of $t + 2 s$ and $2 s + t$ .

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Step 2.4.1

Reorder terms.

$\frac{t (2 s + t) (t - 2 s)}{2 s + t}$

Step 2.4.2

Cancel the common factor.

$\frac{t (2 s + t) (t - 2 s)}{2 s + t}$

Step 2.4.3

Divide $t (t - 2 s)$ by $1$ .

$t (t - 2 s)$

Step 2.5

Apply the distributive property.

$t \cdot t + t (- 2 s)$

Step 2.6

Simplify the expression.

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Step 2.6.1

Multiply $t$ by $t$ .

$t^{2} + t (- 2 s)$

Step 2.6.2

Rewrite using the commutative property of multiplication.

$t^{2} - 2 t s$