Basic Math Examples

$(2 x - \frac{1}{5}) (2 x + \frac{1}{5})$

Step 1

Expand $(2 x - \frac{1}{5}) (2 x + \frac{1}{5})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 x (2 x + \frac{1}{5}) - \frac{1}{5} (2 x + \frac{1}{5})$

Step 1.2

Apply the distributive property.

$2 x (2 x) + 2 x \frac{1}{5} - \frac{1}{5} (2 x + \frac{1}{5})$

Step 1.3

Apply the distributive property.

$2 x (2 x) + 2 x \frac{1}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

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.

$2 \cdot 2 x \cdot x + 2 x \frac{1}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.2.1

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \frac{1}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x \frac{1}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.3

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \frac{1}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.4

Multiply $2 x \frac{1}{5}$ .

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Step 2.1.4.1

Combine $2$ and $\frac{1}{5}$ .

$4 x^{2} + x \frac{2}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.4.2

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

$4 x^{2} + \frac{x \cdot 2}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.5

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

$4 x^{2} + \frac{2 \cdot x}{5} - \frac{1}{5} (2 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.6

Multiply $- \frac{1}{5} (2 x)$ .

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Step 2.1.6.1

Multiply $2$ by $- 1$ .

$4 x^{2} + \frac{2 x}{5} - 2 (\frac{1}{5}) x - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.6.2

Combine $- 2$ and $\frac{1}{5}$ .

$4 x^{2} + \frac{2 x}{5} + \frac{- 2}{5} x - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.6.3

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

$4 x^{2} + \frac{2 x}{5} + \frac{- 2 x}{5} - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.7

Move the negative in front of the fraction.

$4 x^{2} + \frac{2 x}{5} - \frac{2 x}{5} - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.8

Multiply $- \frac{1}{5} \cdot \frac{1}{5}$ .

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Step 2.1.8.1

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

$4 x^{2} + \frac{2 x}{5} - \frac{2 x}{5} - \frac{1}{5 \cdot 5}$

Step 2.1.8.2

Multiply $5$ by $5$ .

$4 x^{2} + \frac{2 x}{5} - \frac{2 x}{5} - \frac{1}{25}$

Step 2.2

Subtract $\frac{2 x}{5}$ from $\frac{2 x}{5}$ .

$4 x^{2} + 0 - \frac{1}{25}$

Step 2.3

Add $4 x^{2}$ and $0$ .

$4 x^{2} - \frac{1}{25}$