# How do you simplify (x + 1)(x - 1)?

Jun 22, 2018

${x}^{2} - 1$

#### Explanation:

Before we attempt to multiply this out, what do you notice about the binomial given?

If fits the difference of squares pattern $\left(a + b\right) \left(a - b\right)$, which has an expansion of $\textcolor{b l u e}{{a}^{2} - {b}^{2}}$.

Essentially, our $a = x$ and our $b = 1$. We can plug these into our blue expression to get

${x}^{2} - 1$

Now, every product of binomials won't be in this form, but we can use FOIL (Firsts, Outsides, Insides, Lasts), which will work every time. This is the order we multiply in.

• Multiply the first terms: $x \cdot x = {x}^{2}$
• Multiply the outside terms: $x \cdot - 1 = - x$
• Multiply the inside terms: $1 \cdot x = x$
• Multiply the last term: $1 \cdot - 1 = - 1$

This is equal to

${x}^{2} + x - x - 1$

The middle terms cancel, and we're left with

${x}^{2} - 1$

Remember, FOIL will work every time, but if we see a product of binomials of the form $\left(a + b\right) \left(a - b\right)$, we can immediately recognize that it fits the difference of squares pattern.

Hope this helps!