Basic Math Examples

$(\frac{1}{3} \cdot \frac{t - (B - y)}{t}) \cdot (\frac{1}{3} t - \frac{1}{3} \cdot (B - y))$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\frac{1}{3} \cdot \frac{t - B - - y}{t} \cdot (\frac{1}{3} t - \frac{1}{3} \cdot (B - y))$

Step 1.2

Multiply $- - y$ .

Tap for more steps...

Step 1.2.1

Multiply $- 1$ by $- 1$ .

$\frac{1}{3} \cdot \frac{t - B + 1 y}{t} \cdot (\frac{1}{3} t - \frac{1}{3} \cdot (B - y))$

Step 1.2.2

Multiply $y$ by $1$ .

$\frac{1}{3} \cdot \frac{t - B + y}{t} \cdot (\frac{1}{3} t - \frac{1}{3} \cdot (B - y))$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Multiply $\frac{1}{3}$ by $\frac{t - B + y}{t}$ .

$\frac{t - B + y}{3 t} \cdot (\frac{1}{3} t - \frac{1}{3} \cdot (B - y))$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Combine $\frac{1}{3}$ and $t$ .

$\frac{t - B + y}{3 t} \cdot (\frac{t}{3} - \frac{1}{3} \cdot (B - y))$

Step 2.2.2

Apply the distributive property.

$\frac{t - B + y}{3 t} \cdot (\frac{t}{3} - \frac{1}{3} B - \frac{1}{3} (- y))$

Step 2.2.3

Combine $B$ and $\frac{1}{3}$ .

$\frac{t - B + y}{3 t} \cdot (\frac{t}{3} - \frac{B}{3} - \frac{1}{3} (- y))$

Step 2.2.4

Multiply $- \frac{1}{3} (- y)$ .

Tap for more steps...

Step 2.2.4.1

Multiply $- 1$ by $- 1$ .

$\frac{t - B + y}{3 t} \cdot (\frac{t}{3} - \frac{B}{3} + 1 (\frac{1}{3}) y)$

Step 2.2.4.2

Multiply $\frac{1}{3}$ by $1$ .

$\frac{t - B + y}{3 t} \cdot (\frac{t}{3} - \frac{B}{3} + \frac{1}{3} y)$

Step 2.2.4.3

Combine $\frac{1}{3}$ and $y$ .

$\frac{t - B + y}{3 t} \cdot (\frac{t}{3} - \frac{B}{3} + \frac{y}{3})$

Step 2.3

Multiply $\frac{t - B + y}{3 t}$ by $\frac{t}{3} - \frac{B}{3} + \frac{y}{3}$ .

$\frac{(t - B + y) (\frac{t}{3} - \frac{B}{3} + \frac{y}{3})}{3 t}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Combine the numerators over the common denominator.

$\frac{(t - B + y) (\frac{t - B}{3} + \frac{y}{3})}{3 t}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{(t - B + y) \frac{t - B + y}{3}}{3 t}$

Step 3.3

Reorder $t$ and $- B$ .

$\frac{(t - B + y) \frac{- B + t + y}{3}}{3 t}$

Step 4

Factor $\frac{- B + t + y}{3}$ out of $\frac{(t - B + y) \frac{- B + t + y}{3}}{3 t}$ .

$\frac{- B + t + y}{3} \cdot \frac{t - B + y}{3 t}$

Step 5

Multiply $\frac{- B + t + y}{3} \cdot \frac{t - B + y}{3 t}$ .

Tap for more steps...

Step 5.1

Multiply $\frac{- B + t + y}{3}$ by $\frac{t - B + y}{3 t}$ .

$\frac{(- B + t + y) (t - B + y)}{3 (3 t)}$

Step 5.2

Reorder terms.

$\frac{(- B + t + y) (- B + t + y)}{3 (3 t)}$

Step 5.3

Raise $- B + t + y$ to the power of $1$ .

$\frac{{(- B + t + y)}^{1} (- B + t + y)}{3 (3 t)}$

Step 5.4

Raise $- B + t + y$ to the power of $1$ .

$\frac{{(- B + t + y)}^{1} {(- B + t + y)}^{1}}{3 (3 t)}$

Step 5.5

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

$\frac{{(- B + t + y)}^{1 + 1}}{3 (3 t)}$

Step 5.6

Add $1$ and $1$ .

$\frac{{(- B + t + y)}^{2}}{3 (3 t)}$

Step 5.7

Multiply $3$ by $3$ .

$\frac{{(- B + t + y)}^{2}}{9 t}$