Basic Math Examples

$- 9 t (- 2 t^{2} + 5)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$- 9 t (- 2 t^{2}) - 9 t \cdot 5$

Step 1.2

Simplify the expression.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$- 9 \cdot - 2 t \cdot t^{2} - 9 t \cdot 5$

Step 1.2.2

Multiply $5$ by $- 9$ .

$- 9 \cdot - 2 t \cdot t^{2} - 45 t$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $t^{2}$ .

$- 9 \cdot - 2 (t^{2} t) - 45 t$

Step 2.1.2

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

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Step 2.1.2.1

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

$- 9 \cdot - 2 (t^{2} t^{1}) - 45 t$

Step 2.1.2.2

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

$- 9 \cdot - 2 t^{2 + 1} - 45 t$

Step 2.1.3

Add $2$ and $1$ .

$- 9 \cdot - 2 t^{3} - 45 t$

Step 2.2

Multiply $- 9$ by $- 2$ .

$18 t^{3} - 45 t$