Factoring Equations

Question

Factor 25x²-9n² completely.

Answer 1

25x^2-9n^2

(5x)^2-(3n)^2

(5x+3n)(5x-3n)

Answer 2

What he have is the difference of two squares: 25 is 5² and 9 is 3².

When we have Do2S, the answer becomes: (a + b)(a - b). That way, the middle term cancels out (ab - ab).

So our final answer is:

(5x + 3n)(5x - 3n)

 

You can check this is true by FOILing it back out.