Difference of Squares Sample Question

Solution:

It would take a significant amount of time to square the values in the numerator and then subtract them. An easier approach is to notice that the numerator is in the form of a difference of squares:

${\mathrm{x}}^2-{\mathrm{y}}^2=\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}-\mathrm{y}\right)$. Here, x = 555, and y = 55.

$\begin{array}{l}\Rightarrow \frac{{\left(555\right)}^2-{\left(55\right)}^2}{500}\\ \Rightarrow \frac{\left(555+55\right)\left(555-55\right)}{500}\\ \Rightarrow \frac{\left(610\right)\left(\cancel{500}\right)}{\cancel{500}}\\ \Rightarrow 610\end{array}$