Q.222. - Intermediate Algebra

Question

Solve the square using the binomial squares pattern.

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

Step-by-Step Solution

Answer

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

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 - b 2 = a 2 - 2 a b + b 2 .

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