SOLUTION: factor 25(x+3)^2-9(x-1)^2 16(x+1)^2-9(x+2)^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor 25(x+3)^2-9(x-1)^2 16(x+1)^2-9(x+2)^2      Log On


   

Question 77977This question is from textbook algebra structue and method
: factor
25(x+3)^2-9(x-1)^2

16(x+1)^2-9(x+2)^2 This question is from textbook algebra structue and method

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since these expressions represent a difference of squares, we can use that identity. For instance, 25%28x%2B3%29%5E2-9%28x-1%29%5E2 is equivalent to
5%5E2%28x%2B3%29%5E2-3%5E2%28x-1%29%5E2
which can be written as
%285%28x%2B3%29%29%5E2-%283%28x-1%29%29%5E2
So now we use the difference of squares formula to get


So 5%5E2%28x%2B3%29%5E2-3%5E2%28x-1%29%5E2 factors to
%285%28x%2B3%29%2B3%28x-1%29%29%285%28x%2B3%29-3%28x-1%29%29
------------------------------------------------------
The same idea can be applied to 16%28x%2B1%29%5E2-9%28x%2B2%29%5E2

16%28x%2B1%29%5E2-9%28x%2B2%29%5E2
4%5E2%28x%2B1%29%5E2-3%5E2%28x%2B2%29%5E2



So 16%28x%2B1%29%5E2-9%28x%2B2%29%5E2 factors to
%284%28x%2B1%29%2B3%28x%2B2%29%29%284%28x%2B1%29-3%28x%2B2%29%29