Question

Solve the square using the binomial squares pattern.

${\left(\frac{1}{5}x-\frac{1}{7}y\right)}^2$

Short answer

The solution is$\frac{1}{25}{x}^2-\frac{2}{35}xy+\frac{1}{49}{y}^2$.

Step-by-step solution

Step 1. Given information.

The given expression is${\left(\frac{1}{5}x-\frac{1}{7}y\right)}^2$.

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

Solve it as follows:

$$\begin{gathered} {\left(\frac{1}{5}x-\frac{1}{7}y\right)}^2={\left(\frac{1}{5}x\right)}^2-2\times \frac{1}{5}x\times \frac{1}{7}y+{\left(\frac{1}{7}y\right)}^2 \\ \Rightarrow \frac{1}{25}{x}^2-\frac{2}{35}xy+\frac{1}{49}{y}^2 \end{gathered}$$

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are$\frac{1}{25}{x}^2-\frac{2}{35}xy+\frac{1}{49}{y}^2$.