Needing help understanding steps

Question

I am trying to study for the accuplacer, but I am not understanding the steps to get the answers to some problems. 

 

1. solve for n:   a²+n+2b²=(a+b)(a+2b)

 

2. (x³y⁵-xy⁴+x²y²) / (xy)

 

3. (x⁵y⁷-xy⁴) / (xy)

 

4. x³+6x+8x

 

5. t(t-2)-3t(t-2)

 

 

Any help is appreciated! If there are any links that might help me to understand these questions is welcomed too. 

Answer 1

1.  a²+n+2b²=(a+b)(a+2b)

 

a² +n +2b² = a² + 2ab + ab + 2b²

a² +n +2b² = a² + 3ab + 2b²

So n = 3ab

 

2.  (x³y⁵-xy⁴+x²y²)/xy = xy*(x²y⁴-y³+xy)/xy = x²y⁴ - y³ + xy   for all x,y ≠ 0

 

3.  (x⁵y⁷ - xy⁴)/xy = (x⁴y⁶ - y³)*xy/xy = x⁴y⁶ - y³    for all x,y ≠ 0

 

4.  x³+6x+8x = x³+14x

 

5.  t(t-2) - 3t(t-2) = (t-3t)(t-2) = (-2t)(t-2)