Question

Factorise $\frac{\left(x^2-y^2\right)}{100}$

Answer 1

We need to factorize $\frac{\left(x^2-y^2\right)}{100}$:

$$\begin{gathered} \frac{\left(x^2-y^2\right)}{100} \\ ={\left(\frac{x}{10}\right)}^2-{\left(\frac{y}{10}\right)}^2 \\ =\left(\frac{x}{10}+\frac{y}{10}\right)\left(\frac{x}{10}-\frac{x}{10}\right)\left[\because a^2-b^2=(a+b)(a-b)\right] \\ =\left(\frac{x+y}{10}\right)\left(\frac{x-y}{10}\right) \end{gathered}$$

Hence, the factors of $\frac{\left(x^2-y^2\right)}{100}$ are $\left(\frac{x+y}{10}\right)$ and $\left(\frac{x-y}{10}\right)$