How do I completely factor expressions

Question

Please help since I am confused on how to do this.

 

   How do I compete factor   144 - 9p^2   ?

 

   Please show steps.  Thanks!

Answer 1

One way to factor is to find its factors. The other is to recall that (a+x)(a-x)=a^2-ax+ax-x^2=a^2-x^2. In this case you do both.

 

144 is a square as is 9p^2. So if you look at the form factor, the way to factor this is:

(12+3p)(12-3p). Since each expression is divisible by 3, this is completely factored to: 9(4+p)(4-p).