algebra/trig help pleeeeeeeeeeeease?

Question

i have an algebra trig. problem i can't figure out.

simplify:

(x^2 - 4)^1/2 (3) (2x+1)^2 (2) + (2x+1)^3 (1/2) (x^2 - 4)^-1/2 (2x)

the answer in the book says:
(2x+1)^2 (8x^2 + x - 24) OVER (x^2 - 4)^1/2


im so stuck. can someone help me get from the problem to the answer?

Answer 1

(x^2 - 4)^1/2 (3) (2x+1)^2 (2) +(2x+1)^3 (1/2)(x^2 -4)^-1/2

multiply with (x^2 - 4)^1/2/(x^2 - 4)^1/2
6 (x^2 - 4)(2x + 1)^2 + x(2x + 1)^3/(x^2 - 4)^1/2
(2x+1)^2(6(x^2 - 4) + x(2x + 1))/(x^2 - 4)^1/2
(2x+1)^2((6x^2 - 24 + 2x^2 + x))/(x^2 - 4)^1/2
(2x + 1)^2[8x^2 + x -24]/(x^2 - 4)^1/2

Answer 2

hi,
I guess i got the answer..
step:1
(x^2 - 4)^1/2 (6) (2x+1)^2 + (2x+1)^3 (x^2 - 4)^-1/2 (x)
here I simply multiplied 3 and 2 as 6 in the first part and slashed 2x into x in the second part.

step:2
[(x^2 - 4) (6) (2x+1)^2 + (2x+1)^3 (x)] / (x^2 - 4)^1/2
here we took (x^2 - 4)^1/2 as common denominator (I studied this subject in my native language so bear if there's any mistake.. lolz)

step3: [(2x+1)^2 (6x^2 - 24 + 2x^2 + x)] / (x^2 - 4)^1/2
here I took (2x+1)^2 out from up and simplified inner bracket

Step 4: (2x+1)^2 (8x^2 + x - 24) / (x^2 - 4)^1/2
derived answer

Answer 3

Well, I just spent about ten or fifteen minutes on it and I can't get it, though I should have been able to. It's odd that the answer doesn't involve an x^3 in it since 2x+1 is cubed. That's the only problem I had with it. Everything else I understand. If I figure it out later though I will tell you.

Answer 4

(x^2 - 4)^1/2 (3) (2x+1)^2 (2) + (2x+1)^3 (1/2) (x^2 - 4)^-1/2 (2x)

I think you mean this:
6(x^2-4)^.5( 2x+1)^2 + x(2x+1)^3(x^2-4)^-.5
=[6(x^2-4)(2x+1)^2 + x(2x+1)^3]/(x^2-4)^.5
= (2x+1)^2[6(x^2-4) + x(2x+1)]/(x^2-4)^.5
= {(2x+1)^2 [6x^2-24 +2x^2+x}/ (x^2-4x)^.5
= (2x+1)^2(8x^2+x-24)/(x^2-4x)^.5