Algebra Examples

$y = 5 {(x + \frac{1}{5})}^{2} - \frac{26}{5}$

Simplify each term.

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Rewrite ${(x + \frac{1}{5})}^{2}$ as $(x + \frac{1}{5}) (x + \frac{1}{5})$ .

$y = 5 ((x + \frac{1}{5}) (x + \frac{1}{5})) - \frac{26}{5}$

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

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Apply the distributive property.

$y = 5 (x (x + \frac{1}{5}) + \frac{1}{5} \cdot (x + \frac{1}{5})) - \frac{26}{5}$

Apply the distributive property.

$y = 5 (x x + x (\frac{1}{5}) + \frac{1}{5} \cdot (x + \frac{1}{5})) - \frac{26}{5}$

Apply the distributive property.

$y = 5 (x x + x (\frac{1}{5}) + (\frac{1}{5} x + \frac{1}{5} \cdot \frac{1}{5})) - \frac{26}{5}$

Remove parentheses.

$y = 5 (x x + x (\frac{1}{5}) + \frac{1}{5} x + \frac{1}{5} \cdot \frac{1}{5}) - \frac{26}{5}$

Simplify and combine like terms.

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Simplify each term.

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Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 5 (x^{1 + 1} + x (\frac{1}{5}) + \frac{1}{5} x + \frac{1}{5} \cdot \frac{1}{5}) - \frac{26}{5}$

Add $1$ and $1$ to get $2$ .

$y = 5 (x^{2} + x (\frac{1}{5}) + \frac{1}{5} x + \frac{1}{5} \cdot \frac{1}{5}) - \frac{26}{5}$

Simplify $x \frac{1}{5}$ .

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Write $x$ as a fraction with denominator $1$ .

$y = 5 (x^{2} + \frac{x}{1} \cdot \frac{1}{5} + \frac{1}{5} x + \frac{1}{5} \cdot \frac{1}{5}) - \frac{26}{5}$

Multiply $\frac{x}{1}$ and $\frac{1}{5}$ to get $\frac{x}{5}$ .

$y = 5 (x^{2} + \frac{x}{5} + \frac{1}{5} x + \frac{1}{5} \cdot \frac{1}{5}) - \frac{26}{5}$

Simplify $\frac{1}{5} x$ .

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Write $x$ as a fraction with denominator $1$ .

$y = 5 (x^{2} + \frac{x}{5} + \frac{1}{5} \cdot \frac{x}{1} + \frac{1}{5} \cdot \frac{1}{5}) - \frac{26}{5}$

Multiply $\frac{1}{5}$ and $\frac{x}{1}$ to get $\frac{x}{5}$ .

$y = 5 (x^{2} + \frac{x}{5} + \frac{x}{5} + \frac{1}{5} \cdot \frac{1}{5}) - \frac{26}{5}$

Simplify $\frac{1}{5} \frac{1}{5}$ .

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Multiply $\frac{1}{5}$ and $\frac{1}{5}$ to get $\frac{1}{5 \cdot 5}$ .

$y = 5 (x^{2} + \frac{x}{5} + \frac{x}{5} + \frac{1}{5 \cdot 5}) - \frac{26}{5}$

Multiply $5$ by $5$ to get $25$ .

$y = 5 (x^{2} + \frac{x}{5} + \frac{x}{5} + \frac{1}{25}) - \frac{26}{5}$

Add $\frac{x}{5}$ and $\frac{x}{5}$ to get $2 \frac{x}{5}$ .

$y = 5 (x^{2} + 2 (\frac{x}{5}) + \frac{1}{25}) - \frac{26}{5}$

Simplify $2 \frac{x}{5}$ .

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Write $2$ as a fraction with denominator $1$ .

$y = 5 (x^{2} + \frac{2}{1} \cdot \frac{x}{5} + \frac{1}{25}) - \frac{26}{5}$

Multiply $\frac{2}{1}$ and $\frac{x}{5}$ to get $\frac{2 x}{5}$ .

$y = 5 (x^{2} + \frac{2 x}{5} + \frac{1}{25}) - \frac{26}{5}$

Apply the distributive property.

$y = 5 x^{2} + 5 (\frac{2 x}{5}) + 5 (\frac{1}{25}) - \frac{26}{5}$

Simplify.

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Cancel the common factor of $5$ .

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Write $5$ as a fraction with denominator $1$ .

$y = 5 x^{2} + \frac{5}{1} \cdot \frac{2 x}{5} + 5 (\frac{1}{25}) - \frac{26}{5}$

Factor out the greatest common factor $5$ .

$y = 5 x^{2} + \frac{5 \cdot 1}{1} \cdot \frac{2 x}{5 \cdot 1} + 5 (\frac{1}{25}) - \frac{26}{5}$

Cancel the common factor.

$y = 5 x^{2} + \frac{5 \cdot 1}{1} \cdot \frac{2 x}{5 \cdot 1} + 5 (\frac{1}{25}) - \frac{26}{5}$

Rewrite the expression.

$y = 5 x^{2} + \frac{1}{1} \cdot \frac{2 x}{1} + 5 (\frac{1}{25}) - \frac{26}{5}$

Simplify.

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Multiply $\frac{1}{1}$ and $\frac{2 x}{1}$ to get $\frac{2 x}{1}$ .

$y = 5 x^{2} + \frac{2 x}{1} + 5 (\frac{1}{25}) - \frac{26}{5}$

Divide $2 x$ by $1$ to get $2 x$ .

$y = 5 x^{2} + 2 x + 5 (\frac{1}{25}) - \frac{26}{5}$

Cancel the common factor of $5$ .

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Write $5$ as a fraction with denominator $1$ .

$y = 5 x^{2} + 2 x + \frac{5}{1} \cdot \frac{1}{25} - \frac{26}{5}$

Factor out the greatest common factor $5$ .

$y = 5 x^{2} + 2 x + \frac{5 \cdot 1}{1} \cdot \frac{1}{5 \cdot 5} - \frac{26}{5}$

Cancel the common factor.

$y = 5 x^{2} + 2 x + \frac{5 \cdot 1}{1} \cdot \frac{1}{5 \cdot 5} - \frac{26}{5}$

Rewrite the expression.

$y = 5 x^{2} + 2 x + \frac{1}{1} \cdot \frac{1}{5} - \frac{26}{5}$

Multiply $\frac{1}{1}$ and $\frac{1}{5}$ to get $\frac{1}{5}$ .

$y = 5 x^{2} + 2 x + \frac{1}{5} - \frac{26}{5}$

Combine the numerators over the common denominator.

$y = 5 x^{2} + 2 x + \frac{1 - 1 \cdot 26}{5}$

Simplify the numerator.

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Multiply $- 1$ by $26$ to get $- 26$ .

$y = 5 x^{2} + 2 x + \frac{1 - 26}{5}$

Subtract $26$ from $1$ .

$y = 5 x^{2} + 2 x + \frac{- 25}{5}$

Divide $- 25$ by $5$ to get $- 5$ .

$y = 5 x^{2} + 2 x - 5$

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