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.

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

Apply the distributive property.

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

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

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

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

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

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

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

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

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

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

Multiply $5$ by $5$ .

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

Add $\frac{x}{5}$ and $\frac{x}{5}$ .

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

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

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

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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Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

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Factor $5$ out of $25$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine fractions.

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Combine fractions with similar denominators.

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

Simplify the expression.

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Subtract $26$ from $1$ .

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

Divide $- 25$ by $5$ .

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

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