Question

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

Answer 1

`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 `(a+b)(a-b)`, which has an expansion of `color(blue)(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*x=x^2`
• Multiply the outside terms: `x*-1=-x`
• Multiply the inside terms: `1*x=x`
• Multiply the last term: `1*-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 `(a+b)(a-b)`, we can immediately recognize that it fits the difference of squares pattern.

Hope this helps!