# What is the product of (x/4-1/3)*(x/4+1/3)?

Nov 24, 2016

$\frac{9 {x}^{2} - 16}{144}$

#### Explanation:

First, get all of the fractions over a common denominator by multiplying by the appropriate form of $1$:

$\left(\left(\frac{3}{3}\right) \left(\frac{x}{4}\right) - \left(\frac{4}{4}\right) \left(\frac{1}{3}\right)\right) \cdot \left(\left(\frac{3}{3}\right) \left(\frac{x}{4}\right) + \left(\frac{4}{4}\right) \left(\frac{1}{3}\right)\right) \implies$

$\left(\frac{3 x}{12} - \frac{4}{12}\right) \cdot \left(\frac{3 x}{12} + \frac{4}{12}\right) \implies$

$\frac{3 x - 4}{12} \cdot \frac{3 x + 4}{12}$

Now we can cross multiply the numerators and multiply the denominators:

$\left(9 {x}^{2} - 12 x + 12 x - 16\right) 144 \implies$

$\frac{9 {x}^{2} - 16}{144}$