Algebra Examples

$(z - \frac{5}{3}) (z - \frac{2}{3})$

Step 1

Expand $(z - \frac{5}{3}) (z - \frac{2}{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$z (z - \frac{2}{3}) - \frac{5}{3} (z - \frac{2}{3})$

Step 1.2

Apply the distributive property.

$z \cdot z + z (- \frac{2}{3}) - \frac{5}{3} (z - \frac{2}{3})$

Step 1.3

Apply the distributive property.

$z \cdot z + z (- \frac{2}{3}) - \frac{5}{3} z - \frac{5}{3} (- \frac{2}{3})$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $z$ by $z$ .

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

Step 2.1.2

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

$z^{2} - \frac{z \cdot 2}{3} - \frac{5}{3} z - \frac{5}{3} (- \frac{2}{3})$

Step 2.1.3

Move $2$ to the left of $z$ .

$z^{2} - \frac{2 \cdot z}{3} - \frac{5}{3} z - \frac{5}{3} (- \frac{2}{3})$

Step 2.1.4

Combine $z$ and $\frac{5}{3}$ .

$z^{2} - \frac{2 z}{3} - \frac{z \cdot 5}{3} - \frac{5}{3} (- \frac{2}{3})$

Step 2.1.5

Move $5$ to the left of $z$ .

$z^{2} - \frac{2 z}{3} - \frac{5 \cdot z}{3} - \frac{5}{3} (- \frac{2}{3})$

Step 2.1.6

Multiply $- \frac{5}{3} (- \frac{2}{3})$ .

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Step 2.1.6.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.6.2

Multiply $\frac{5}{3}$ by $1$ .

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

Step 2.1.6.3

Multiply $\frac{5}{3}$ by $\frac{2}{3}$ .

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

Step 2.1.6.4

Multiply $5$ by $2$ .

$z^{2} - \frac{2 z}{3} - \frac{5 z}{3} + \frac{10}{3 \cdot 3}$

Step 2.1.6.5

Multiply $3$ by $3$ .

$z^{2} - \frac{2 z}{3} - \frac{5 z}{3} + \frac{10}{9}$

Step 2.2

Combine the numerators over the common denominator.

$z^{2} + \frac{- 2 z - 5 z}{3} + \frac{10}{9}$

Step 3

Subtract $5 z$ from $- 2 z$ .

$z^{2} + \frac{- 7 z}{3} + \frac{10}{9}$

Step 4

Move the negative in front of the fraction.

$z^{2} - \frac{7 z}{3} + \frac{10}{9}$