Can anyone help??? PLZ!!!!!!!!!! factoring expressions?

Question

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

2. (x^2 +1)^(1/2) + 2(x^2 +1)^(-1/2)

3. (a^2 +1)^2 - 7(a^2 +1) +10

4. 3x^2( 4x-12)^2 + x^3(2)(4x-12)(4)

5. 3(2x-1)^2 (2) (x+3)^(1/2) + (2x-1)^3 (1/2) (x+3)^(-1/2)

Answer 1

It will take a long time to write it all out. If you want to email me, I've kept my notes.

1. [(x + 1)^2]/x^(3/2)

2. (x^2 + 3)/sqrt(x^2 + 1)

3. (a + 2)(a - 2)(a + 1)(a - 1)

4. 16x^2(x - 3)(5x - 9)

5. [2(2x - 1)^2(5x + 8)]/(x + 3)^(1/2)

Edit: I received an email from you, and couldn't get it to send, so I'm going to write out the notes here.

1. x^(-3/2) + 2x^(-1/2) + x^(1/2) = 1/x^(3/2) + 2/x^(1/2) + x^(1/2)

To work this type of problem, find a common denominator. In this one, the denominator on each needs to be x^(3/2)  After doing this, it becomes:

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

= (1 + 2x +  x^2)/x^(3/2)

= [(x + 1)^2]/x^(3/2)

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

2.  (x^2 +1)^(1/2) + 2(x^2 +1)^(-1/2) = (x^2 +1)^(1/2) + 2/[(x^2 +1)^(1/2)]

Use the same method as the previous problem, finding a common denominator which is (x^2 +1)^(1/2)

[(x^2 +1)^(1/2)*(x^2 +1)^(1/2)]/(x^2 +1)^(1/2)  +  2/[(x^2 +1)^(1/2)]

= [(x^2 +1) + 2]/(x^2 +1)^(1/2)

= (x^2 + 3)/(x^2 +1)^(1/2)

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

3. (a^2 +1)^2 - 7(a^2 +1) +10

= a^4 - 5a^2 + 4

= (a^2 - 4)(a^2 - 1)

=  (a + 2)(a - 2)(a + 1)(a - 1)

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

4. 3x^2( 4x-12)^2 + x^3(2)(4x-12)(4)

= 80x^4 - 384x^3 + 432x^2

= 16x^2(5x^2 -24x + 27)

= 16x^2(x - 3)(5x - 9)

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

5.  3(2x-1)^2 (2) (x+3)^(1/2) + (2x-1)^3 (1/2) (x+3)^(-1/2)

= [2*6*(x+3)^(1/2)*(x+3)^(1/2)]/2*(x+3)^(1... + [(2x - 1)^3]/2(x+3)^(1/2)

= [12(x + 3)(2x-1)^2 + [(2x - 1)^3]/2(x+3)^(1/2)

= [2(2x - 1)^2(5x + 8)]/(x + 3)^(1/2)