Basic Math Examples

$4 t^{5} (2 t^{3} - t^{2} + t)$

Step 1

Apply the distributive property.

$4 t^{5} (2 t^{3}) + 4 t^{5} (- t^{2}) + 4 t^{5} t$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 2 t^{5} t^{3} + 4 t^{5} (- t^{2}) + 4 t^{5} t$

Step 2.2

Rewrite using the commutative property of multiplication.

$4 \cdot 2 t^{5} t^{3} + 4 \cdot - 1 t^{5} t^{2} + 4 t^{5} t$

Step 2.3

Multiply $t^{5}$ by $t$ by adding the exponents.

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Step 2.3.1

Move $t$ .

$4 \cdot 2 t^{5} t^{3} + 4 \cdot - 1 t^{5} t^{2} + 4 (t \cdot t^{5})$

Step 2.3.2

Multiply $t$ by $t^{5}$ .

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Step 2.3.2.1

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

$4 \cdot 2 t^{5} t^{3} + 4 \cdot - 1 t^{5} t^{2} + 4 (t^{1} t^{5})$

Step 2.3.2.2

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

$4 \cdot 2 t^{5} t^{3} + 4 \cdot - 1 t^{5} t^{2} + 4 t^{1 + 5}$

Step 2.3.3

Add $1$ and $5$ .

$4 \cdot 2 t^{5} t^{3} + 4 \cdot - 1 t^{5} t^{2} + 4 t^{6}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $t^{3}$ .

$4 \cdot 2 (t^{3} t^{5}) + 4 \cdot - 1 t^{5} t^{2} + 4 t^{6}$

Step 3.1.2

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

$4 \cdot 2 t^{3 + 5} + 4 \cdot - 1 t^{5} t^{2} + 4 t^{6}$

Step 3.1.3

Add $3$ and $5$ .

$4 \cdot 2 t^{8} + 4 \cdot - 1 t^{5} t^{2} + 4 t^{6}$

Step 3.2

Multiply $4$ by $2$ .

$8 t^{8} + 4 \cdot - 1 t^{5} t^{2} + 4 t^{6}$

Step 3.3

Multiply $t^{5}$ by $t^{2}$ by adding the exponents.

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Step 3.3.1

Move $t^{2}$ .

$8 t^{8} + 4 \cdot - 1 (t^{2} t^{5}) + 4 t^{6}$

Step 3.3.2

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

$8 t^{8} + 4 \cdot - 1 t^{2 + 5} + 4 t^{6}$

Step 3.3.3

Add $2$ and $5$ .

$8 t^{8} + 4 \cdot - 1 t^{7} + 4 t^{6}$

Step 3.4

Multiply $4$ by $- 1$ .

$8 t^{8} - 4 t^{7} + 4 t^{6}$