could someone help me understand this?

Question

Factor the following trinomial.

 

20x²+41xa+20a²

Answer 1

 

Look for 2 factors of the first and last termd

 

    Factors of 20x²

 

        4x * 5x

       10x * 2x

       20x * x

 

     Factors of 20a²

 

        4a * 5a

       10a * 2a

       20a * a

 

Since all terms are positive, we know that all of the factored terms are positive also

 

After trial and error, and using FOIL to verify, we find that the factored expression is

  

     (5x + 4a)(4x + 5a)

 

     F => 5x * 4x = 20x²

     O=> 5x * 5a = 25xa

     I => 4a * 4a = 16a²

     L => 4a * 5a = 20a²

 

Simplifying this results in the original expression.