Algebra Examples

$4 x^{2} - 4 x + 1$

Step 1

Factor out the $4$

$4 (x^{2} - x + \frac{1}{4})$

Step 2

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

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Step 2.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1.1

Apply the product rule to $- \frac{1}{2}$ .

${(- 1)}^{2} {(\frac{1}{2})}^{2}$

Step 2.1.2

Apply the product rule to $\frac{1}{2}$ .

${(- 1)}^{2} \frac{1^{2}}{2^{2}}$

Step 2.2

Raise $- 1$ to the power of $2$ .

$1 \frac{1^{2}}{2^{2}}$

Step 2.3

Multiply $\frac{1^{2}}{2^{2}}$ by $1$ .

$\frac{1^{2}}{2^{2}}$

Step 2.4

One to any power is one.

$\frac{1}{2^{2}}$

Step 2.5

Raise $2$ to the power of $2$ .

$\frac{1}{4}$

Step 3

Add $\frac{1}{4}$ to get the perfect square trinomial.

$4 (x^{2} - x + \frac{1}{4} + \frac{1}{4})$

Step 4

Simplify.

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Step 4.1

Combine the numerators over the common denominator.

$4 (x^{2} - x + \frac{1 + 1}{4})$

Step 4.2

Add $1$ and $1$ .

$4 (x^{2} - x + \frac{2}{4})$

Step 4.3

Cancel the common factor of $2$ and $4$ .

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Step 4.3.1

Factor $2$ out of $2$ .

$4 (x^{2} - x + \frac{2 (1)}{4})$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $4$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

$4 (x^{2} - x + \frac{1}{2})$

Step 4.4

Apply the distributive property.

$4 x^{2} + 4 (- x) + 4 (\frac{1}{2})$

Step 4.5

Simplify.

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Step 4.5.1

Multiply $- 1$ by $4$ .

$4 x^{2} - 4 x + 4 (\frac{1}{2})$

Step 4.5.2

Cancel the common factor of $2$ .

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Step 4.5.2.1

Factor $2$ out of $4$ .

$4 x^{2} - 4 x + 2 (2) \frac{1}{2}$

Step 4.5.2.2

Cancel the common factor.

$4 x^{2} - 4 x + 2 \cdot 2 \frac{1}{2}$

Step 4.5.2.3

Rewrite the expression.

$4 x^{2} - 4 x + 2$