SOLUTION: Expand (\sqrt{z} + 2z)^4+(\sqrt{z} - 2z)^4.

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Question 1035391: Expand (\sqrt{z} + 2z)^4+(\sqrt{z} - 2z)^4.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you meant %28sqrt%28z%29+%2B+2z%29%5E4+%2B+%28sqrt%28z%29+-+2z%29%5E4.
The first term, when expanded, will consist of five terms with positive signs.
The second term, when expanded, will look like the expansion of the first term, except that the signs alternate (+,-,+,-,+). This means that, when you add them together, the second and fourth terms cancel but the first, third, and fifth terms are multiplied by 2.
==>
= 2z%5E2+%2B+12z%2A4z%5E2+%2B+2%2A16z%5E4
= 2z%5E2+%2B+48z%5E3+%2B+32z%5E4