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

1 Answer
Jun 22, 2018

Answer:

#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!