SOLUTION: It asks to factor the following. a^2-9. I had a difficult time with this one. I would really appreciate the help!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: It asks to factor the following. a^2-9. I had a difficult time with this one. I would really appreciate the help!      Log On


   

Question 147452This question is from textbook algebra
: It asks to factor the following. a^2-9. I had a difficult time with this one. I would really appreciate the help! This question is from textbook algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2-9 Start with the given expression

%28a%29%5E2-9 Rewrite a%5E2 as %28a%29%5E2

%28a%29%5E2-%283%29%5E2 Rewrite 9 as %283%29%5E2


Now use the difference of squares. Remember, the difference of squares formula is A%5E2-B%5E2=%28A%2BB%29%28A-B%29 where in this case A=a and B=3

a%5E2-9=%28a%2B3%29%28a-3%29 Plug in A=a and B=3

So the expression

a%5E2-9

factors to

%28a%2B3%29%28a-3%29

Notice that if you foil the factored expression, you get the original expression. This verifies our answer.