Basic Math Examples

$(- 4 t^{2} + 36 t) \cdot (t - 9)$

Step 1

Expand $(- 4 t^{2} + 36 t) (t - 9)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 4 t^{2} (t - 9) + 36 t (t - 9)$

Step 1.2

Apply the distributive property.

$- 4 t^{2} t - 4 t^{2} \cdot - 9 + 36 t (t - 9)$

Step 1.3

Apply the distributive property.

$- 4 t^{2} t - 4 t^{2} \cdot - 9 + 36 t \cdot t + 36 t \cdot - 9$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $t$ .

$- 4 (t \cdot t^{2}) - 4 t^{2} \cdot - 9 + 36 t \cdot t + 36 t \cdot - 9$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

$- 4 (t^{1} t^{2}) - 4 t^{2} \cdot - 9 + 36 t \cdot t + 36 t \cdot - 9$

Step 2.1.1.2.2

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

$- 4 t^{1 + 2} - 4 t^{2} \cdot - 9 + 36 t \cdot t + 36 t \cdot - 9$

Step 2.1.1.3

Add $1$ and $2$ .

$- 4 t^{3} - 4 t^{2} \cdot - 9 + 36 t \cdot t + 36 t \cdot - 9$

Step 2.1.2

Multiply $- 9$ by $- 4$ .

$- 4 t^{3} + 36 t^{2} + 36 t \cdot t + 36 t \cdot - 9$

Step 2.1.3

Multiply $t$ by $t$ by adding the exponents.

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Step 2.1.3.1

Move $t$ .

$- 4 t^{3} + 36 t^{2} + 36 (t \cdot t) + 36 t \cdot - 9$

Step 2.1.3.2

Multiply $t$ by $t$ .

$- 4 t^{3} + 36 t^{2} + 36 t^{2} + 36 t \cdot - 9$

Step 2.1.4

Multiply $- 9$ by $36$ .

$- 4 t^{3} + 36 t^{2} + 36 t^{2} - 324 t$

Step 2.2

Add $36 t^{2}$ and $36 t^{2}$ .

$- 4 t^{3} + 72 t^{2} - 324 t$