Basic Math Examples

$(3 x - \frac{1}{5}) (3 x + \frac{1}{5})$

Step 1

Expand $(3 x - \frac{1}{5}) (3 x + \frac{1}{5})$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$3 x (3 x + \frac{1}{5}) - \frac{1}{5} (3 x + \frac{1}{5})$

Step 1.2

Apply the distributive property.

$3 x (3 x) + 3 x \frac{1}{5} - \frac{1}{5} (3 x + \frac{1}{5})$

Step 1.3

Apply the distributive property.

$3 x (3 x) + 3 x \frac{1}{5} - \frac{1}{5} (3 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \frac{1}{5} - \frac{1}{5} (3 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \frac{1}{5} - \frac{1}{5} (3 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \frac{1}{5} - \frac{1}{5} (3 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.4

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

Tap for more steps...

Step 2.1.4.1

Combine $3$ and $\frac{1}{5}$ .

$9 x^{2} + x \frac{3}{5} - \frac{1}{5} (3 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.4.2

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

$9 x^{2} + \frac{x \cdot 3}{5} - \frac{1}{5} (3 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.5

Move $3$ to the left of $x$ .

$9 x^{2} + \frac{3 \cdot x}{5} - \frac{1}{5} (3 x) - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.6

Multiply $- \frac{1}{5} (3 x)$ .

Tap for more steps...

Step 2.1.6.1

Multiply $3$ by $- 1$ .

$9 x^{2} + \frac{3 x}{5} - 3 (\frac{1}{5}) x - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.6.2

Combine $- 3$ and $\frac{1}{5}$ .

$9 x^{2} + \frac{3 x}{5} + \frac{- 3}{5} x - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.6.3

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

$9 x^{2} + \frac{3 x}{5} + \frac{- 3 x}{5} - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.7

Move the negative in front of the fraction.

$9 x^{2} + \frac{3 x}{5} - \frac{3 x}{5} - \frac{1}{5} \cdot \frac{1}{5}$

Step 2.1.8

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

Tap for more steps...

Step 2.1.8.1

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

$9 x^{2} + \frac{3 x}{5} - \frac{3 x}{5} - \frac{1}{5 \cdot 5}$

Step 2.1.8.2

Multiply $5$ by $5$ .

$9 x^{2} + \frac{3 x}{5} - \frac{3 x}{5} - \frac{1}{25}$

Step 2.2

Subtract $\frac{3 x}{5}$ from $\frac{3 x}{5}$ .

$9 x^{2} + 0 - \frac{1}{25}$

Step 2.3

Add $9 x^{2}$ and $0$ .

$9 x^{2} - \frac{1}{25}$