SOLUTION: Factor fully (2m-3)^2-(8m^2-4)^2

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Question 1131329: Factor fully (2m-3)^2-(8m^2-4)^2
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Same as: Quadratic_Equations/1131330: 

Again, you don't need to FOIL the BINOMIALS.

Again, this is a DIFFERENCE of TWO SQUARES <======> 

The same concept applies!!

Correct answer:  

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
 .


(2m-3)^2 - (8m^2-4)^2.


     Use the general formula   -  = (a+b)*(a-b), which is valid for any numbers "a" and "b".

     In this case,  a = (2m-3),  b = ,  so


     a + b =  = .

     a - b =  =  = -(2m-1)*(4m+1).


Therefore,

(2m-3)^2 - (8m^2-4)^2 = .      ANSWER





Solved.





--------------------





The key idea and the lesson to learn is THIS :






     Use the formula   -  = (a+b)*(a-b).





And there is nothing interesting after that - only the mechanical work.







 

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