I want solve this inequations

> solve((1/4*(beta^2-6))*(-beta^2+2*alpha) > 0);

After running, maple gives an answer in four lines

alpha < (1/2)*beta^2     0 < -(1/2)*beta^2+3
(1/2)*beta^2 < alpha     -(1/2)*beta^2 < -3
[]                                 beta = -sqrt(6)
[]                                 beta = sqrt(6)

now I have questions:

1) In spite of knowing range of beta in thhe second parts of first two lines of answer, why maple...

I write this code:

> e1 := a-3;
                             a - 3
> e2 := sqrt(6)*b+6;
                           (1/2)      
                          6      b + 6
> trac := e1+e2;
                                 (1/2)  
                        a + 3 + 6      b
> dter := e1*e2;
                             / (1/2)      \
                     (a - 3) \6      b + 6/
> dell := trac^2-4*dter;
                           2                           

I explain my problem with an example:

When I write

sort(3x^3+x^2+x+1);

the answer is

      3    2        
 3 x  + x  + x + 1

 But when I write

sort((x+1)(x+2))

answer is

x(x+2)+1

while I want this form:

   2          
 x  + 2 x + 1

Even when I type only

(x+1)(x+2)

into a blank page, again the answer is 

x(x+2)+1

not 

I have a system with two nonlinear inequality. How can I solve the system?