Algebra Examples

$x^{2} + x y + y^{2}$

Step 1

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 1.1

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

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

Step 1.2

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

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

Step 2

Add $\frac{y^{2}}{4}$ to get the perfect square trinomial.

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Step 2.1

To write $y^{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{2} + x y + y^{2} \cdot \frac{4}{4} + \frac{y^{2}}{4}$

Step 2.2

Combine $y^{2}$ and $\frac{4}{4}$ .

$x^{2} + x y + \frac{y^{2} \cdot 4}{4} + \frac{y^{2}}{4}$

Step 2.3

Combine the numerators over the common denominator.

$x^{2} + x y + \frac{y^{2} \cdot 4 + y^{2}}{4}$

Step 2.4

Add $y^{2} \cdot 4$ and $y^{2}$ .

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Step 2.4.1

Reorder $y^{2}$ and $4$ .

$x^{2} + x y + \frac{4 \cdot y^{2} + y^{2}}{4}$

Step 2.4.2

Add $4 \cdot y^{2}$ and $y^{2}$ .

$x^{2} + x y + \frac{5 \cdot y^{2}}{4}$

$x^{2} + x y + \frac{5 y^{2}}{4}$