Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $5$ by $5$ .

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

Step 2.1.4

Cancel the common factor of $5$ .

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Step 2.1.4.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

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

Step 2.1.4.2

Factor $5$ out of $5 x$ .

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

Step 2.1.4.3

Cancel the common factor.

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

Step 2.1.4.4

Rewrite the expression.

$25 x^{2} + x \cdot - 1 + \frac{1}{5} (5 x) + \frac{1}{5} (- \frac{1}{5})$

Step 2.1.5

Move $- 1$ to the left of $x$ .

$25 x^{2} - 1 \cdot x + \frac{1}{5} (5 x) + \frac{1}{5} (- \frac{1}{5})$

Step 2.1.6

Rewrite $- 1 x$ as $- x$ .

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

Step 2.1.7

Cancel the common factor of $5$ .

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Step 2.1.7.1

Factor $5$ out of $5 x$ .

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

Step 2.1.7.2

Cancel the common factor.

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

Step 2.1.7.3

Rewrite the expression.

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

Step 2.1.8

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

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Step 2.1.8.1

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

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

Step 2.1.8.2

Multiply $5$ by $5$ .

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

Step 2.2

Add $- x$ and $x$ .

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

Step 2.3

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

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