Basic Math Examples

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

Step 1

Rewrite ${(y - \frac{4}{9})}^{2}$ as $(y - \frac{4}{9}) (y - \frac{4}{9})$ .

$(y - \frac{4}{9}) (y - \frac{4}{9})$

Step 2

Expand $(y - \frac{4}{9}) (y - \frac{4}{9})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$y (y - \frac{4}{9}) - \frac{4}{9} (y - \frac{4}{9})$

Step 2.2

Apply the distributive property.

$y \cdot y + y (- \frac{4}{9}) - \frac{4}{9} (y - \frac{4}{9})$

Step 2.3

Apply the distributive property.

$y \cdot y + y (- \frac{4}{9}) - \frac{4}{9} y - \frac{4}{9} (- \frac{4}{9})$

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 $y$ by $y$ .

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

Step 3.1.2

Combine $y$ and $\frac{4}{9}$ .

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

Step 3.1.3

Move $4$ to the left of $y$ .

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

Step 3.1.4

Combine $y$ and $\frac{4}{9}$ .

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

Step 3.1.5

Move $4$ to the left of $y$ .

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

Step 3.1.6

Multiply $- \frac{4}{9} (- \frac{4}{9})$ .

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Step 3.1.6.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.6.2

Multiply $\frac{4}{9}$ by $1$ .

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

Step 3.1.6.3

Multiply $\frac{4}{9}$ by $\frac{4}{9}$ .

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

Step 3.1.6.4

Multiply $4$ by $4$ .

$y^{2} - \frac{4 y}{9} - \frac{4 y}{9} + \frac{16}{9 \cdot 9}$

Step 3.1.6.5

Multiply $9$ by $9$ .

$y^{2} - \frac{4 y}{9} - \frac{4 y}{9} + \frac{16}{81}$

Step 3.2

Subtract $\frac{4 y}{9}$ from $- \frac{4 y}{9}$ .

$y^{2} - 2 \frac{4 y}{9} + \frac{16}{81}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 2 \frac{4 y}{9}$ .

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Step 4.1.1

Combine $- 2$ and $\frac{4 y}{9}$ .

$y^{2} + \frac{- 2 (4 y)}{9} + \frac{16}{81}$

Step 4.1.2

Multiply $4$ by $- 2$ .

$y^{2} + \frac{- 8 y}{9} + \frac{16}{81}$

Step 4.2

Move the negative in front of the fraction.

$y^{2} - \frac{8 y}{9} + \frac{16}{81}$