Question 282933
The binomial x²-81 is called a _________ of two__________, and will factor in to(______)(_______)?

{{{x^2-81}}} is called a difference of two squares. The formula is {{{a^2-b^2=(a+b)(a-b)}}}. You can check by foiling (a+b)(a-b).  When you foil (a+b)(a-b) you get {{{a^2-ab+ab-b^2}}} the -ab and the +ab cancel out. Leaving you {{{a^2-b^2}}}. 

In the binomial {{{x^2-81}}}, {{{x^2}}} is a perfect square and so is 81.  The square root of {{{x^2}}} is x and the square root of 81 is 9. {{{x^2-81}}}={{{x^2-9^2}}}, that factors to (x+9)(x-9).  So to check you can foil (x+9)(x-9) you get {{{x^2-9x+9x-81}}}, the -9x and the +9x cancel and you have your original binomial. {{{x^2-81}}}.

The answer is: The binomial {{{x^2-81}}} is called a difference of two squares, and will factor in to (x+9)(x-9).