Basic Math Examples

$(t - \frac{1}{5}) (t^{2} - \frac{1}{5})$

Step 1

Expand $(t - \frac{1}{5}) (t^{2} - \frac{1}{5})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$t (t^{2} - \frac{1}{5}) - \frac{1}{5} (t^{2} - \frac{1}{5})$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$t^{1} t^{2} + t (- \frac{1}{5}) - \frac{1}{5} t^{2} - \frac{1}{5} (- \frac{1}{5})$

Step 2.1.1.1.2

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

$t^{1 + 2} + t (- \frac{1}{5}) - \frac{1}{5} t^{2} - \frac{1}{5} (- \frac{1}{5})$

Step 2.1.1.2

Add $1$ and $2$ .

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

Step 2.1.2

Combine $t$ and $\frac{1}{5}$ .

$t^{3} - \frac{t}{5} - \frac{1}{5} t^{2} - \frac{1}{5} (- \frac{1}{5})$

Step 2.1.3

Combine $t^{2}$ and $\frac{1}{5}$ .

$t^{3} - \frac{t}{5} - \frac{t^{2}}{5} - \frac{1}{5} (- \frac{1}{5})$

Step 2.1.4

Multiply $- \frac{1}{5} (- \frac{1}{5})$ .

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Step 2.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.4.2

Multiply $\frac{1}{5}$ by $1$ .

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

Step 2.1.4.3

Multiply $\frac{1}{5}$ by $\frac{1}{5}$ .

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

Step 2.1.4.4

Multiply $5$ by $5$ .

$t^{3} - \frac{t}{5} - \frac{t^{2}}{5} + \frac{1}{25}$

Step 2.2

Move $- \frac{t}{5}$ .

$t^{3} - \frac{t^{2}}{5} - \frac{t}{5} + \frac{1}{25}$