Consider $100x^{2}-9$. Rewrite $100x^{2}-9$ as $\left(10x\right)^{2}-3^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $9$ and $25$ is $225$. Multiply $\frac{4x^{2}}{9}$ times $\frac{25}{25}$. Multiply $\frac{1}{25}$ times $\frac{9}{9}$.
$$\frac{25\times 4x^{2}}{225}-\frac{9}{225}$$
Since $\frac{25\times 4x^{2}}{225}$ and $\frac{9}{225}$ have the same denominator, subtract them by subtracting their numerators.
