Basic Math Examples

$a \cdot a^{2} - a^{3}$

Step 1

Factor $a^{3}$ out of $a \cdot a^{2} - a^{3}$ .

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Step 1.1

Factor $a^{3}$ out of $a \cdot a^{2}$ .

$a^{3} (a^{- 2} \cdot a^{2}) - a^{3}$

Step 1.2

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

$a^{3} (a^{- 2} \cdot a^{2}) + a^{3} \cdot - 1$

Step 1.3

Factor $a^{3}$ out of $a^{3} (a^{- 2} \cdot a^{2}) + a^{3} \cdot - 1$ .

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

Step 2

Multiply $a^{- 2}$ by $a^{2}$ by adding the exponents.

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Step 2.1

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

$a^{3} (a^{- 2 + 2} - 1)$

Step 2.2

Add $- 2$ and $2$ .

$a^{3} (a^{0} - 1)$

Step 3

Simplify $a^{0}$ .

$a^{3} (1 - 1)$

Step 4

Subtract $1$ from $1$ .

$a^{3} \cdot 0$