Basic Math Examples

$- 3 t {(t - 3)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 3$ by $3$ .

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

Step 2.1.2

Raise $- 3$ to the power of $2$ .

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

Step 2.1.3

Multiply $9$ by $3$ .

$- 3 t (t^{3} - 9 t^{2} + 27 t + {(- 3)}^{3})$

Step 2.1.4

Raise $- 3$ to the power of $3$ .

$- 3 t (t^{3} - 9 t^{2} + 27 t - 27)$

Step 2.2

Apply the distributive property.

$- 3 t \cdot t^{3} - 3 t (- 9 t^{2}) - 3 t (27 t) - 3 t \cdot - 27$

Step 3

Simplify.

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Step 3.1

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

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Step 3.1.1

Move $t^{3}$ .

$- 3 (t^{3} t) - 3 t (- 9 t^{2}) - 3 t (27 t) - 3 t \cdot - 27$

Step 3.1.2

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

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Step 3.1.2.1

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

$- 3 (t^{3} t^{1}) - 3 t (- 9 t^{2}) - 3 t (27 t) - 3 t \cdot - 27$

Step 3.1.2.2

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

$- 3 t^{3 + 1} - 3 t (- 9 t^{2}) - 3 t (27 t) - 3 t \cdot - 27$

Step 3.1.3

Add $3$ and $1$ .

$- 3 t^{4} - 3 t (- 9 t^{2}) - 3 t (27 t) - 3 t \cdot - 27$

Step 3.2

Rewrite using the commutative property of multiplication.

$- 3 t^{4} - 3 \cdot - 9 t \cdot t^{2} - 3 t (27 t) - 3 t \cdot - 27$

Step 3.3

Rewrite using the commutative property of multiplication.

$- 3 t^{4} - 3 \cdot - 9 t \cdot t^{2} - 3 \cdot 27 t \cdot t - 3 t \cdot - 27$

Step 3.4

Multiply $- 27$ by $- 3$ .

$- 3 t^{4} - 3 \cdot - 9 t \cdot t^{2} - 3 \cdot 27 t \cdot t + 81 t$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $t^{2}$ .

$- 3 t^{4} - 3 \cdot - 9 (t^{2} t) - 3 \cdot 27 t \cdot t + 81 t$

Step 4.1.2

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

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Step 4.1.2.1

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

$- 3 t^{4} - 3 \cdot - 9 (t^{2} t^{1}) - 3 \cdot 27 t \cdot t + 81 t$

Step 4.1.2.2

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

$- 3 t^{4} - 3 \cdot - 9 t^{2 + 1} - 3 \cdot 27 t \cdot t + 81 t$

Step 4.1.3

Add $2$ and $1$ .

$- 3 t^{4} - 3 \cdot - 9 t^{3} - 3 \cdot 27 t \cdot t + 81 t$

Step 4.2

Multiply $- 3$ by $- 9$ .

$- 3 t^{4} + 27 t^{3} - 3 \cdot 27 t \cdot t + 81 t$

Step 4.3

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

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Step 4.3.1

Move $t$ .

$- 3 t^{4} + 27 t^{3} - 3 \cdot 27 (t \cdot t) + 81 t$

Step 4.3.2

Multiply $t$ by $t$ .

$- 3 t^{4} + 27 t^{3} - 3 \cdot 27 t^{2} + 81 t$

Step 4.4

Multiply $- 3$ by $27$ .

$- 3 t^{4} + 27 t^{3} - 81 t^{2} + 81 t$