Algebra Examples

$y = 2 {(x + \frac{5}{4})}^{2} - \frac{49}{8}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Rewrite ${(x + \frac{5}{4})}^{2}$ as $(x + \frac{5}{4}) (x + \frac{5}{4})$ .

$y = 2 ((x + \frac{5}{4}) (x + \frac{5}{4})) - \frac{49}{8}$

Step 2.2

Expand $(x + \frac{5}{4}) (x + \frac{5}{4})$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$y = 2 (x (x + \frac{5}{4}) + \frac{5}{4} \cdot (x + \frac{5}{4})) - \frac{49}{8}$

Step 2.2.2

Apply the distributive property.

$y = 2 (x \cdot x + x (\frac{5}{4}) + \frac{5}{4} \cdot (x + \frac{5}{4})) - \frac{49}{8}$

Step 2.2.3

Apply the distributive property.

$y = 2 (x \cdot x + x (\frac{5}{4}) + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$y = 2 (x^{2} + x (\frac{5}{4}) + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Step 2.3.1.2

Combine $x$ and $\frac{5}{4}$ .

$y = 2 (x^{2} + \frac{x \cdot 5}{4} + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Step 2.3.1.3

Move $5$ to the left of $x$ .

$y = 2 (x^{2} + \frac{5 \cdot x}{4} + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Step 2.3.1.4

Combine $\frac{5}{4}$ and $x$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Step 2.3.1.5

Multiply $\frac{5}{4} \cdot \frac{5}{4}$ .

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Step 2.3.1.5.1

Multiply $\frac{5}{4}$ by $\frac{5}{4}$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{5 \cdot 5}{4 \cdot 4}) - \frac{49}{8}$

Step 2.3.1.5.2

Multiply $5$ by $5$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{25}{4 \cdot 4}) - \frac{49}{8}$

Step 2.3.1.5.3

Multiply $4$ by $4$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{25}{16}) - \frac{49}{8}$

Step 2.3.2

Add $\frac{5 x}{4}$ and $\frac{5 x}{4}$ .

$y = 2 (x^{2} + 2 (\frac{5 x}{4}) + \frac{25}{16}) - \frac{49}{8}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $4$ .

$y = 2 (x^{2} + 2 (\frac{5 x}{2 (2)}) + \frac{25}{16}) - \frac{49}{8}$

Step 2.4.2

Cancel the common factor.

$y = 2 (x^{2} + 2 (\frac{5 x}{2 \cdot 2}) + \frac{25}{16}) - \frac{49}{8}$

Step 2.4.3

Rewrite the expression.

$y = 2 (x^{2} + \frac{5 x}{2} + \frac{25}{16}) - \frac{49}{8}$

Step 2.5

Apply the distributive property.

$y = 2 x^{2} + 2 (\frac{5 x}{2}) + 2 (\frac{25}{16}) - \frac{49}{8}$

Step 2.6

Simplify.

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Step 2.6.1

Cancel the common factor of $2$ .

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Step 2.6.1.1

Cancel the common factor.

$y = 2 x^{2} + 2 (\frac{5 x}{2}) + 2 (\frac{25}{16}) - \frac{49}{8}$

Step 2.6.1.2

Rewrite the expression.

$y = 2 x^{2} + 5 x + 2 (\frac{25}{16}) - \frac{49}{8}$

Step 2.6.2

Cancel the common factor of $2$ .

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Step 2.6.2.1

Factor $2$ out of $16$ .

$y = 2 x^{2} + 5 x + 2 (\frac{25}{2 (8)}) - \frac{49}{8}$

Step 2.6.2.2

Cancel the common factor.

$y = 2 x^{2} + 5 x + 2 (\frac{25}{2 \cdot 8}) - \frac{49}{8}$

Step 2.6.2.3

Rewrite the expression.

$y = 2 x^{2} + 5 x + \frac{25}{8} - \frac{49}{8}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$y = 2 x^{2} + 5 x + \frac{25 - 49}{8}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Subtract $49$ from $25$ .

$y = 2 x^{2} + 5 x + \frac{- 24}{8}$

Step 3.2.2

Divide $- 24$ by $8$ .

$y = 2 x^{2} + 5 x - 3$

Step 4