Question

Solve the square using the binomial squares pattern.

${\left(y+\frac{1}{4}\right)}^2$

Short answer

The solution is$y^2+\frac{y}{2}+\frac{1}{16}$.

Step-by-step solution

Step 1. Given information.

The given expression is${\left(y+\frac{1}{4}\right)}^2$.

Step 2. Simplify the given expression by using the binomial squares pattern a+b2=a2+2ab+b2.

Solve it as follows:

$$\begin{gathered} {\left(y+\frac{1}{4}\right)}^2={\left(y\right)}^2+2\times y\times \frac{1}{4}+{\left(\frac{1}{2}\right)}^2 \\ \Rightarrow y^2+\frac{y}{2}+\frac{1}{16} \end{gathered}$$

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are$y^2+\frac{y}{2}+\frac{1}{16}$.