Basic Math Examples

$5 a^{3} + 6 a - 3 a^{2} \cdot (- 5 a)$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

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

Step 1.2

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

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Step 1.2.1

Move $a$ .

$5 a^{3} + 6 a - 3 \cdot - 5 (a \cdot a^{2})$

Step 1.2.2

Multiply $a$ by $a^{2}$ .

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Step 1.2.2.1

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

$5 a^{3} + 6 a - 3 \cdot - 5 (a^{1} a^{2})$

Step 1.2.2.2

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

$5 a^{3} + 6 a - 3 \cdot - 5 a^{1 + 2}$

Step 1.2.3

Add $1$ and $2$ .

$5 a^{3} + 6 a - 3 \cdot - 5 a^{3}$

Step 1.3

Multiply $- 3$ by $- 5$ .

$5 a^{3} + 6 a + 15 a^{3}$

Step 2

Add $5 a^{3}$ and $15 a^{3}$ .

$20 a^{3} + 6 a$