Basic Math Examples

$(12 t^{6} - 8 t^{8}) \div 2 t^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{12 t^{6} - 8 t^{8}}{2 t^{3}}$

Step 2

Factor $4 t^{6}$ out of $12 t^{6} - 8 t^{8}$ .

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Step 2.1

Factor $4 t^{6}$ out of $12 t^{6}$ .

$\frac{4 t^{6} (3) - 8 t^{8}}{2 t^{3}}$

Step 2.2

Factor $4 t^{6}$ out of $- 8 t^{8}$ .

$\frac{4 t^{6} (3) + 4 t^{6} (- 2 t^{2})}{2 t^{3}}$

Step 2.3

Factor $4 t^{6}$ out of $4 t^{6} (3) + 4 t^{6} (- 2 t^{2})$ .

$\frac{4 t^{6} (3 - 2 t^{2})}{2 t^{3}}$

Step 3

Cancel the common factor of $4$ and $2$ .

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Step 3.1

Factor $2$ out of $4 t^{6} (3 - 2 t^{2})$ .

$\frac{2 (2 t^{6} (3 - 2 t^{2}))}{2 t^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{2 (2 t^{6} (3 - 2 t^{2}))}{2 (t^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (2 t^{6} (3 - 2 t^{2}))}{2 t^{3}}$

Step 3.2.3

Rewrite the expression.

$\frac{2 t^{6} (3 - 2 t^{2})}{t^{3}}$

Step 4

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

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Step 4.1

Factor $t^{3}$ out of $2 t^{6} (3 - 2 t^{2})$ .

$\frac{t^{3} (2 t^{3} (3 - 2 t^{2}))}{t^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{t^{3} (2 t^{3} (3 - 2 t^{2}))}{t^{3} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{t^{3} (2 t^{3} (3 - 2 t^{2}))}{t^{3} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{2 t^{3} (3 - 2 t^{2})}{1}$

Step 4.2.4

Divide $2 t^{3} (3 - 2 t^{2})$ by $1$ .

$2 t^{3} (3 - 2 t^{2})$

Step 5

Apply the distributive property.

$2 t^{3} \cdot 3 + 2 t^{3} (- 2 t^{2})$

Step 6

Multiply $3$ by $2$ .

$6 t^{3} + 2 t^{3} (- 2 t^{2})$

Step 7

Rewrite using the commutative property of multiplication.

$6 t^{3} + 2 \cdot - 2 t^{3} t^{2}$

Step 8

Simplify each term.

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Step 8.1

Multiply $t^{3}$ by $t^{2}$ by adding the exponents.

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Step 8.1.1

Move $t^{2}$ .

$6 t^{3} + 2 \cdot - 2 (t^{2} t^{3})$

Step 8.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 t^{3} + 2 \cdot - 2 t^{2 + 3}$

Step 8.1.3

Add $2$ and $3$ .

$6 t^{3} + 2 \cdot - 2 t^{5}$

Step 8.2

Multiply $2$ by $- 2$ .

$6 t^{3} - 4 t^{5}$