SOLUTION: Can the below be factored since it does not have all like characters? 4a^2 + 16ab + 16b^2 = Also, have I correctly factored ax^2 -a = To be a(a+1)(a-1) Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can the below be factored since it does not have all like characters? 4a^2 + 16ab + 16b^2 = Also, have I correctly factored ax^2 -a = To be a(a+1)(a-1) Thank you      Log On


   

Question 1167462: Can the below be factored since it does not have all like characters?
4a^2 + 16ab + 16b^2 =
Also, have I correctly factored ax^2 -a = To be a(a+1)(a-1)
Thank you
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
this is 4(a^2+4ab+4b^2)
that is 4(a+2b)(a+2b) or 4(a+2b)^2
the other ix a(x^2-1)=a (x+1)(x-1)
a(a+1)(a-1) has an a^3 term

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.

1)   Can the below be factored since it does not have all like characters?     4a^2 + 16ab + 16b^2 

    Yes it can be factored.

        4a^2 + 16ab + 16b^2  =  (2a + 4b)^2.


2)   Also, have I correctly factored ax^2 -a = To be a(a+1)(a-1) 

    Your "factoring" is WRONG.

    The correct factoring is  ax^2 -a = a*(x+1)*(x-1).

Solved and answered.

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By the way,  when you pose your question this way 
    Can the below be factored since it does not have all like characters?
    4a^2 + 16ab + 16b^2

you make several logical/mathematical errors simultaneously.


First is that  " it does not have all like characters ".
            In contrary,  it has the common factor 4.


Second,  in order for an expression could be factored,  it is  NOT  NECESSARY  to have all like characters:
            a^2 - b^2 = (a+b)*(a-b).