Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

Multiply $c$ by $c$ by adding the exponents.

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Step 2.1.2.1

Move $c$ .

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

Step 2.1.2.2

Multiply $c$ by $c$ .

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

Step 2.1.3

Multiply $5$ by $5$ .

$25 c^{2} + 5 c (- \frac{2}{3}) + \frac{2}{3} (5 c) + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.4

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

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Step 2.1.4.1

Multiply $- 1$ by $5$ .

$25 c^{2} - 5 c \frac{2}{3} + \frac{2}{3} (5 c) + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.4.2

Combine $- 5$ and $\frac{2}{3}$ .

$25 c^{2} + c \frac{- 5 \cdot 2}{3} + \frac{2}{3} (5 c) + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.4.3

Multiply $- 5$ by $2$ .

$25 c^{2} + c \frac{- 10}{3} + \frac{2}{3} (5 c) + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.4.4

Combine $c$ and $\frac{- 10}{3}$ .

$25 c^{2} + \frac{c \cdot - 10}{3} + \frac{2}{3} (5 c) + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.5

Move $- 10$ to the left of $c$ .

$25 c^{2} + \frac{- 10 \cdot c}{3} + \frac{2}{3} (5 c) + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.6

Move the negative in front of the fraction.

$25 c^{2} - \frac{10 \cdot c}{3} + \frac{2}{3} (5 c) + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.7

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

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Step 2.1.7.1

Combine $5$ and $\frac{2}{3}$ .

$25 c^{2} - \frac{10 c}{3} + \frac{5 \cdot 2}{3} c + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.7.2

Multiply $5$ by $2$ .

$25 c^{2} - \frac{10 c}{3} + \frac{10}{3} c + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.7.3

Combine $\frac{10}{3}$ and $c$ .

$25 c^{2} - \frac{10 c}{3} + \frac{10 c}{3} + \frac{2}{3} (- \frac{2}{3})$

Step 2.1.8

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

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Step 2.1.8.1

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

$25 c^{2} - \frac{10 c}{3} + \frac{10 c}{3} - \frac{2 \cdot 2}{3 \cdot 3}$

Step 2.1.8.2

Multiply $2$ by $2$ .

$25 c^{2} - \frac{10 c}{3} + \frac{10 c}{3} - \frac{4}{3 \cdot 3}$

Step 2.1.8.3

Multiply $3$ by $3$ .

$25 c^{2} - \frac{10 c}{3} + \frac{10 c}{3} - \frac{4}{9}$

Step 2.2

Add $- \frac{10 c}{3}$ and $\frac{10 c}{3}$ .

$25 c^{2} + 0 - \frac{4}{9}$

Step 2.3

Add $25 c^{2}$ and $0$ .

$25 c^{2} - \frac{4}{9}$