Question

How do I factor 25x squared - 64

Answer 1

Its called the Difference of Perfect Squares: 

5 is the square root of 25 
x is the square root of x^2 
(-8)(+8) is the square root of -64 

You can FOIL the factored answer to check your answer: 
First: 5x times 5x = 25x^2 
Outside: (-8 times 5x) = -40x 
Inside: (+8 times 5x) = +40x 
+40x + -40x = 0x so cancel each other out 
Last= -8 times +8 = -64 
So the unfactored expression 
F= 25x^2 
OI= 0 
L= -64 

25x^2-64