Basic Math Examples

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

Step 1

Add $- t^{2}$ and $9 t^{2}$ .

$4 t^{3} (t + 8 t^{2})$

Step 2

Apply the distributive property.

$4 t^{3} t + 4 t^{3} (8 t^{2})$

Step 3

Multiply $t^{3}$ by $t$ by adding the exponents.

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Step 3.1

Move $t$ .

$4 (t \cdot t^{3}) + 4 t^{3} (8 t^{2})$

Step 3.2

Multiply $t$ by $t^{3}$ .

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Step 3.2.1

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

$4 (t^{1} t^{3}) + 4 t^{3} (8 t^{2})$

Step 3.2.2

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

$4 t^{1 + 3} + 4 t^{3} (8 t^{2})$

Step 3.3

Add $1$ and $3$ .

$4 t^{4} + 4 t^{3} (8 t^{2})$

Step 4

Rewrite using the commutative property of multiplication.

$4 t^{4} + 4 \cdot 8 t^{3} t^{2}$

Step 5

Simplify each term.

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Step 5.1

Multiply $t^{3}$ by $t^{2}$ by adding the exponents.

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Step 5.1.1

Move $t^{2}$ .

$4 t^{4} + 4 \cdot 8 (t^{2} t^{3})$

Step 5.1.2

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

$4 t^{4} + 4 \cdot 8 t^{2 + 3}$

Step 5.1.3

Add $2$ and $3$ .

$4 t^{4} + 4 \cdot 8 t^{5}$

Step 5.2

Multiply $4$ by $8$ .

$4 t^{4} + 32 t^{5}$