MHB Solving Exponential Equations: Need Help Understanding 2 Questions

[linapril]

I need help with understanding two questions:
1. (2^x+2)²
The answer I got was: 2^2x+2^x++4, but according to the answers that is wrong. Can any explain why?

2. 8^4x/32^x
I simplified this to become (8⁴/32)^x, but I don't know how to go from there... The answer is apparently 2^7x, but I don't understand how that can be...

Would appreciate the help enormously,
//APRIL

 

[linapril]

Nevermind, I understood question 2 now, but question 1 is still a mystery to me...

 

[Jameson]

I need help with understanding two questions:
1. (2^x+2)²
The answer I got was: 2^2x+2^x++4, but according to the answers that is wrong. Can any explain why?

I think the middle term is wrong. The first and the last terms look good though. Check your work and if you still don't see it then post your attempt and we'll help you sort it out :)

 

[Prove It]

I need help with understanding two questions:
1. (2^x+2)²
The answer I got was: 2^2x+2^x++4, but according to the answers that is wrong. Can any explain why?

2. 8^4x/32^x
I simplified this to become (8⁴/32)^x, but I don't know how to go from there... The answer is apparently 2^7x, but I don't understand how that can be...

Would appreciate the help enormously,
//APRIL

$\displaystyle \begin{align*} \left( 2^x + 2 \right)^2 &= \left( 2^x \right)^2 + 2\cdot 2\cdot 2^x + 2^2 \\ &= 2^{2x} + 2^{x + 2} + 2^2 \end{align*}$