SOLUTION: Today was my first day of intermediate algebra. Our first assignment is factoring polynomials. I am lost and my professor didn't explain much. {{{10a^2-640}}}? :) Please help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Today was my first day of intermediate algebra. Our first assignment is factoring polynomials. I am lost and my professor didn't explain much. {{{10a^2-640}}}? :) Please help.      Log On


   

Question 202331: Today was my first day of intermediate algebra. Our first assignment is factoring polynomials. I am lost and my professor didn't explain much. 10a%5E2-640? :) Please help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
10a%5E2-640 Notice that each term is a multiple of 10, so you can first factor 10.
10%28a%5E2-64%29 Now the binomial (in the parentheses) is the difference of two squares. %28a%29%5E2-%288%29%5E2 and the difference of two squares can be factored thus:
A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29, so apply this concept to the binomial to complete the factoring of the given expression.
highlight%2810a%5E2-640+=+10%28a%2B8%29%28a-8%29%29
To check the solution, you need only multiply the three factors to see that you will arrive at the given expression.
10%2A%28a%2B8%29%28a-8%29+=+10%2A%28a%5E2-8a%2B8a-64%29 which simplifies to:
10%28a%5E2-64%29+=+10a%5E2-640