Algebra Examples

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

Step 1

Combine $\frac{1}{2}$ and $y$ .

$y^{2} + \frac{y}{2}$

Step 2

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

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.2

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 2.2.1

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

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

Step 2.2.2

Multiply $2$ by $2$ .

${(\frac{1}{4})}^{2}$

Step 2.3

Apply the product rule to $\frac{1}{4}$ .

$\frac{1^{2}}{4^{2}}$

Step 2.4

One to any power is one.

$\frac{1}{4^{2}}$

Step 2.5

Raise $4$ to the power of $2$ .

$\frac{1}{16}$

Step 3

Add $\frac{1}{16}$ to get the perfect square trinomial.

$y^{2} + \frac{1}{2} y + \frac{1}{16}$