Basic Math Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $5$ by $2$ .

$10 a^{5} + 2 a^{5} (- 6 a^{3})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$10 a^{5} + 2 \cdot - 6 a^{5} a^{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $a^{5}$ by $a^{3}$ by adding the exponents.

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Step 2.1.1

Move $a^{3}$ .

$10 a^{5} + 2 \cdot - 6 (a^{3} a^{5})$

Step 2.1.2

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

$10 a^{5} + 2 \cdot - 6 a^{3 + 5}$

Step 2.1.3

Add $3$ and $5$ .

$10 a^{5} + 2 \cdot - 6 a^{8}$

Step 2.2

Multiply $2$ by $- 6$ .

$10 a^{5} - 12 a^{8}$