Question

Expand ${(\pi -\frac{22}{7})}^2$ using appropriate identity

Answer 1

Using the identity is $(x-y{)}^2=x^2+y^2-2xy$.

Given: ${(\sqrt{10}x-\sqrt{5}y)}^2$ we apply the above identity by taking $x=\pi$ and $y=-\frac{22}{7}$

We get, ${(\pi -\frac{22}{7})}^2={\left(\pi \right)}^2+{\left(\frac{22}{7}\right)}^2-(2\times \pi \times \frac{22}{7})={\pi }^2+\frac{484}{49}-\frac{44}{7}\pi$

Hence, ${(\pi -\frac{22}{7})}^2={\pi }^2+\frac{484}{49}-\frac{44}{7}\pi$.