Algebra Examples

$H (x) = (- \frac{1}{4} x - 4) (\frac{1}{4} x - 4)$

Step 1

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

$H (x) = a x^{2} + b x + c$

Step 2

Combine fractions.

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Step 2.1

Combine $x$ and $\frac{1}{4}$ .

$H (x) = (- \frac{x}{4} - 4) (\frac{1}{4} x - 4)$

Step 2.2

Combine $\frac{1}{4}$ and $x$ .

$H (x) = (- \frac{x}{4} - 4) (\frac{x}{4} - 4)$

Step 3

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

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Step 3.1

Apply the distributive property.

$H (x) = - \frac{x}{4} \cdot (\frac{x}{4} - 4) - 4 (\frac{x}{4} - 4)$

Step 3.2

Apply the distributive property.

$H (x) = - \frac{x}{4} \cdot \frac{x}{4} - \frac{x}{4} \cdot - 4 - 4 (\frac{x}{4} - 4)$

Step 3.3

Apply the distributive property.

$H (x) = - \frac{x}{4} \cdot \frac{x}{4} - \frac{x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $- \frac{x}{4} \cdot \frac{x}{4}$ .

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Step 4.1.1.1

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

$H (x) = - \frac{x \cdot x}{4 \cdot 4} - \frac{x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.1.2

Raise $x$ to the power of $1$ .

$H (x) = - \frac{x \cdot x}{4 \cdot 4} - \frac{x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.1.3

Raise $x$ to the power of $1$ .

$H (x) = - \frac{x \cdot x}{4 \cdot 4} - \frac{x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.1.4

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

$H (x) = - \frac{x^{1 + 1}}{4 \cdot 4} - \frac{x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.1.5

Add $1$ and $1$ .

$H (x) = - \frac{x^{2}}{4 \cdot 4} - \frac{x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.1.6

Multiply $4$ by $4$ .

$H (x) = - \frac{x^{2}}{16} - \frac{x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.2

Cancel the common factor of $4$ .

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Step 4.1.2.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$H (x) = - \frac{x^{2}}{16} + \frac{- x}{4} \cdot - 4 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.2.2

Factor $4$ out of $- 4$ .

$H (x) = - \frac{x^{2}}{16} + \frac{- x}{4} \cdot (4 (- 1)) - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.2.3

Cancel the common factor.

$H (x) = - \frac{x^{2}}{16} + \frac{- x}{4} \cdot (4 \cdot - 1) - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.2.4

Rewrite the expression.

$H (x) = - \frac{x^{2}}{16} - x \cdot - 1 - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.3

Multiply $- 1$ by $- 1$ .

$H (x) = - \frac{x^{2}}{16} + 1 x - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.4

Multiply $x$ by $1$ .

$H (x) = - \frac{x^{2}}{16} + x - 4 \frac{x}{4} - 4 \cdot - 4$

Step 4.1.5

Cancel the common factor of $4$ .

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Step 4.1.5.1

Factor $4$ out of $- 4$ .

$H (x) = - \frac{x^{2}}{16} + x + 4 (- 1) (\frac{x}{4}) - 4 \cdot - 4$

Step 4.1.5.2

Cancel the common factor.

$H (x) = - \frac{x^{2}}{16} + x + 4 \cdot (- 1 \frac{x}{4}) - 4 \cdot - 4$

Step 4.1.5.3

Rewrite the expression.

$H (x) = - \frac{x^{2}}{16} + x - 1 x - 4 \cdot - 4$

Step 4.1.6

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

$H (x) = - \frac{x^{2}}{16} + x - x - 4 \cdot - 4$

Step 4.1.7

Multiply $- 4$ by $- 4$ .

$H (x) = - \frac{x^{2}}{16} + x - x + 16$

Step 4.2

Subtract $x$ from $x$ .

$H (x) = - \frac{x^{2}}{16} + 0 + 16$

Step 4.3

Add $- \frac{x^{2}}{16}$ and $0$ .

$H (x) = - \frac{x^{2}}{16} + 16$

Step 5

Reorder terms.

$H (x) = - (\frac{1}{16} x^{2}) + 16$

Step 6

Remove parentheses.

$H (x) = - \frac{1}{16} x^{2} + 16$