Basic Math Examples

$(\frac{5}{6} t + \frac{3}{4}) (\frac{5}{6} t - \frac{3}{4})$

Step 1

Combine fractions.

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Step 1.1

Combine $\frac{5}{6}$ and $t$ .

$(\frac{5 t}{6} + \frac{3}{4}) (\frac{5}{6} t - \frac{3}{4})$

Step 1.2

Combine $\frac{5}{6}$ and $t$ .

$(\frac{5 t}{6} + \frac{3}{4}) (\frac{5 t}{6} - \frac{3}{4})$

Step 2

Expand $(\frac{5 t}{6} + \frac{3}{4}) (\frac{5 t}{6} - \frac{3}{4})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{5 t}{6} (\frac{5 t}{6} - \frac{3}{4}) + \frac{3}{4} (\frac{5 t}{6} - \frac{3}{4})$

Step 2.2

Apply the distributive property.

$\frac{5 t}{6} \cdot \frac{5 t}{6} + \frac{5 t}{6} (- \frac{3}{4}) + \frac{3}{4} (\frac{5 t}{6} - \frac{3}{4})$

Step 2.3

Apply the distributive property.

$\frac{5 t}{6} \cdot \frac{5 t}{6} + \frac{5 t}{6} (- \frac{3}{4}) + \frac{3}{4} \cdot \frac{5 t}{6} + \frac{3}{4} (- \frac{3}{4})$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $\frac{5 t}{6} \cdot \frac{5 t}{6} + \frac{5 t}{6} (- \frac{3}{4}) + \frac{3}{4} \cdot \frac{5 t}{6} + \frac{3}{4} (- \frac{3}{4})$ .

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Step 3.1.1

Reorder the factors in the terms $\frac{5 t}{6} (- \frac{3}{4})$ and $\frac{3}{4} \cdot \frac{5 t}{6}$ .

$\frac{5 t}{6} \cdot \frac{5 t}{6} - \frac{3}{4} \cdot \frac{5 t}{6} + \frac{3}{4} \cdot \frac{5 t}{6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.1.2

Add $- \frac{3}{4} \cdot \frac{5 t}{6}$ and $\frac{3}{4} \cdot \frac{5 t}{6}$ .

$\frac{5 t}{6} \cdot \frac{5 t}{6} + 0 + \frac{3}{4} (- \frac{3}{4})$

Step 3.1.3

Add $\frac{5 t}{6} \cdot \frac{5 t}{6}$ and $0$ .

$\frac{5 t}{6} \cdot \frac{5 t}{6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $\frac{5 t}{6} \cdot \frac{5 t}{6}$ .

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Step 3.2.1.1

Multiply $\frac{5 t}{6}$ by $\frac{5 t}{6}$ .

$\frac{5 t (5 t)}{6 \cdot 6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2.1.2

Multiply $5$ by $5$ .

$\frac{25 t \cdot t}{6 \cdot 6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2.1.3

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

$\frac{25 (t^{1} t)}{6 \cdot 6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2.1.4

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

$\frac{25 (t^{1} t^{1})}{6 \cdot 6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2.1.5

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

$\frac{25 t^{1 + 1}}{6 \cdot 6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2.1.6

Add $1$ and $1$ .

$\frac{25 t^{2}}{6 \cdot 6} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2.1.7

Multiply $6$ by $6$ .

$\frac{25 t^{2}}{36} + \frac{3}{4} (- \frac{3}{4})$

Step 3.2.2

Multiply $\frac{3}{4} (- \frac{3}{4})$ .

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Step 3.2.2.1

Multiply $\frac{3}{4}$ by $\frac{3}{4}$ .

$\frac{25 t^{2}}{36} - \frac{3 \cdot 3}{4 \cdot 4}$

Step 3.2.2.2

Multiply $3$ by $3$ .

$\frac{25 t^{2}}{36} - \frac{9}{4 \cdot 4}$

Step 3.2.2.3

Multiply $4$ by $4$ .

$\frac{25 t^{2}}{36} - \frac{9}{16}$