SOLUTION: Factor the following binomial. 25x^2 – 81y^2 Factors: 1,3,5,9,15,25,27,45,75,81,135,225,405,675,2025, -1,-3,-5,-9,-15,-25,-27,-45,-75,-81,-135,-225,-405,-675,-2025, -2025 (-1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the following binomial. 25x^2 – 81y^2 Factors: 1,3,5,9,15,25,27,45,75,81,135,225,405,675,2025, -1,-3,-5,-9,-15,-25,-27,-45,-75,-81,-135,-225,-405,-675,-2025, -2025 (-1      Log On


   

Question 78158: Factor the following binomial.
25x^2 – 81y^2
Factors:
1,3,5,9,15,25,27,45,75,81,135,225,405,675,2025,
-1,-3,-5,-9,-15,-25,-27,-45,-75,-81,-135,-225,-405,-675,-2025,
-2025
(-1)*(2025)=-2025
(-3)*(675)=-2025
(-5)*(405)=-2025
(-9)*(225)=-2025
(-15)*(135)=-2025
(-25)*(81)=-2025
(-27)*(75)=-2025
(-45)*(45)=-2025
a=25,m=45, and n=-45
Did the other stuff and do I end up with this or am I wrong?
(5x+9y) * (5x-9y)

Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the binomial:
25x%5E2-81y%5E2 This is the difference of two squares:%285x%29%5E2-%289y%29%5E2.
The difference of two squares can be factored thus:
A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29 Applying this to the given binomial, you get:
25x%5E2-81y%5E2+=+%285x%2B9y%29%285x-9y%29 which is exactly what your last line shows.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You did this perfectly. Notice how each number is a perfect square, so you can use the difference of squares to find the factors much more quickly.