Basic Math Examples

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - 15 a^{6} t^{2} \div 5 a^{3} t$

Step 1

Rewrite the division as a fraction.

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{15 a^{6} t^{2}}{5 a^{3} t}$

Step 2

Cancel the common factor of $15$ and $5$ .

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Step 2.1

Factor $5$ out of $15 a^{6} t^{2}$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{5 (3 a^{6} t^{2})}{5 a^{3} t}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $5 a^{3} t$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{5 (3 a^{6} t^{2})}{5 (a^{3} t)}$

Step 2.2.2

Cancel the common factor.

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{5 (3 a^{6} t^{2})}{5 (a^{3} t)}$

Step 2.2.3

Rewrite the expression.

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{3 a^{6} t^{2}}{a^{3} t}$

Step 3

Cancel the common factor of $a^{6}$ and $a^{3}$ .

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Step 3.1

Factor $a^{3}$ out of $3 a^{6} t^{2}$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{a^{3} (3 a^{3} t^{2})}{a^{3} t}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{3}$ out of $a^{3} t$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{a^{3} (3 a^{3} t^{2})}{a^{3} (t)}$

Step 3.2.2

Cancel the common factor.

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{a^{3} (3 a^{3} t^{2})}{a^{3} t}$

Step 3.2.3

Rewrite the expression.

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{3 a^{3} t^{2}}{t}$

Step 4

Cancel the common factor of $t^{2}$ and $t$ .

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Step 4.1

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

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{t (3 a^{3} t)}{t}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Raise $t$ to the power of $1$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{t (3 a^{3} t)}{t^{1}}$

Step 4.2.2

Factor $t$ out of $t^{1}$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{t (3 a^{3} t)}{t \cdot 1}$

Step 4.2.3

Cancel the common factor.

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{t (3 a^{3} t)}{t \cdot 1}$

Step 4.2.4

Rewrite the expression.

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - \frac{3 a^{3} t}{1}$

Step 4.2.5

Divide $3 a^{3} t$ by $1$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - (3 a^{3} t)$

Step 5

Multiply $3$ by $- 1$ .

$45 a^{8} t^{9} - 15 a^{6} t^{7} + 25 a^{3} t^{4} - 3 a^{3} t$