Basic Math Examples

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

Step 1

Combine fractions.

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Step 1.1

Combine $\frac{2}{3}$ and $y$ .

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

Step 1.2

Rewrite ${(\frac{2 y}{3} - 3)}^{2}$ as $(\frac{2 y}{3} - 3) (\frac{2 y}{3} - 3)$ .

$(\frac{2 y}{3} - 3) (\frac{2 y}{3} - 3)$

Step 2

Expand $(\frac{2 y}{3} - 3) (\frac{2 y}{3} - 3)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{2 y}{3} (\frac{2 y}{3} - 3) - 3 (\frac{2 y}{3} - 3)$

Step 2.2

Apply the distributive property.

$\frac{2 y}{3} \cdot \frac{2 y}{3} + \frac{2 y}{3} \cdot - 3 - 3 (\frac{2 y}{3} - 3)$

Step 2.3

Apply the distributive property.

$\frac{2 y}{3} \cdot \frac{2 y}{3} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $\frac{2 y}{3} \cdot \frac{2 y}{3}$ .

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Step 3.1.1.1

Multiply $\frac{2 y}{3}$ by $\frac{2 y}{3}$ .

$\frac{2 y (2 y)}{3 \cdot 3} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.1.2

Multiply $2$ by $2$ .

$\frac{4 y \cdot y}{3 \cdot 3} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.1.3

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

$\frac{4 (y^{1} y)}{3 \cdot 3} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.1.4

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

$\frac{4 (y^{1} y^{1})}{3 \cdot 3} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.1.5

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

$\frac{4 y^{1 + 1}}{3 \cdot 3} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.1.6

Add $1$ and $1$ .

$\frac{4 y^{2}}{3 \cdot 3} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.1.7

Multiply $3$ by $3$ .

$\frac{4 y^{2}}{9} + \frac{2 y}{3} \cdot - 3 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.2

Cancel the common factor of $3$ .

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Step 3.1.2.1

Factor $3$ out of $- 3$ .

$\frac{4 y^{2}}{9} + \frac{2 y}{3} \cdot (3 (- 1)) - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.2.2

Cancel the common factor.

$\frac{4 y^{2}}{9} + \frac{2 y}{3} \cdot (3 \cdot - 1) - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.2.3

Rewrite the expression.

$\frac{4 y^{2}}{9} + 2 y \cdot - 1 - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.3

Multiply $- 1$ by $2$ .

$\frac{4 y^{2}}{9} - 2 y - 3 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.4

Cancel the common factor of $3$ .

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Step 3.1.4.1

Factor $3$ out of $- 3$ .

$\frac{4 y^{2}}{9} - 2 y + 3 (- 1) \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.4.2

Cancel the common factor.

$\frac{4 y^{2}}{9} - 2 y + 3 \cdot - 1 \frac{2 y}{3} - 3 \cdot - 3$

Step 3.1.4.3

Rewrite the expression.

$\frac{4 y^{2}}{9} - 2 y - 1 (2 y) - 3 \cdot - 3$

Step 3.1.5

Multiply $2$ by $- 1$ .

$\frac{4 y^{2}}{9} - 2 y - 2 y - 3 \cdot - 3$

Step 3.1.6

Multiply $- 3$ by $- 3$ .

$\frac{4 y^{2}}{9} - 2 y - 2 y + 9$

Step 3.2

Subtract $2 y$ from $- 2 y$ .

$\frac{4 y^{2}}{9} - 4 y + 9$