SOLUTION: Can you explain to me how factoring 36x^2-100 = 4(3x-5)(3x+5) Its alittle confusing to me

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you explain to me how factoring 36x^2-100 = 4(3x-5)(3x+5) Its alittle confusing to me      Log On


   

Question 197177: Can you explain to me how factoring 36x^2-100 = 4(3x-5)(3x+5) Its alittle confusing to me
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
36x%5E2-100 This is difference of 2 squares (36x^2 is 6x*6x) and 100 is 10*10.
Usually that would be enough to say
36x%5E2-100 =
%286x+-10%29%286x%2B10%29 and call is a day. But in this case, you can see that each term includes a common factor of 2.
6x-10 = 2%2A%283x-5%29 etc.
So
%286x+-10%29%286x%2B10%29
2%2A%283x-5%29+%2A+2%2A%283x%2B5%29
4+%2A%283x-5%29%2A%283x%2B5%29

Alternatively, you might have seen that 36 and 100 are both products of 2 squares.
36 = 9*4
100 = 25*4
If you factor out the 4, you are still left with a difference of 2 squares
4%2A%289x%5E2+-+25%29
Which simplifies to the same result.
All this just confirms that in mathematics, there are many ways to get to the same answer (hopefully correct) answer.
Hope that helps