α^4 + β^4 Expansion?

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DaftPunk327
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#1
Report Thread starter 8 years ago
#1
I need to expand [α^4 + β^4 ] in terms of α + β and αβ
but unfortunately my textbook doesn't cover this
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james22
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#2
Report 8 years ago
#2
Start with (a+b)^4.
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DaftPunk327
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#3
Report Thread starter 8 years ago
#3
(Original post by james22)
Start with (a+b)^4.

that's what I did originally, but I ended up with 5 terms, and trying to simplify them all in terms of α + β and αβ became too much of a headache
I'm pretty sure there's a way to do it using
α^2 + β^2 but I've got no idea what it is
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james22
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#4
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#4
(Original post by DaftPunk327)

that's what I did originally, but I ended up with 5 terms, and trying to simplify them all in terms of α + β and αβ became too much of a headache
I'm pretty sure there's a way to do it using
α^2 + β^2 but I've got no idea what it is
You also have to use (a+b)^2, but not yet.

When you expans (a+b)^4 you should be able to write it in terms of a^4+b^4, ab and another term which you need another trick for.
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DaftPunk327
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#5
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#5
(Original post by james22)
You also have to use (a+b)^2, but not yet.

When you expans (a+b)^4 you should be able to write it in terms of a^4+b^4, ab and another term which you need another trick for.
okay

so I'm getting:

a^2 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

(a^4+b^4) + 6(ab)^2 + 4ab(a^2+b^2)
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james22
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#6
Report 8 years ago
#6
(Original post by DaftPunk327)
okay

so I'm getting:

a^2 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

(a^4+b^4) + 6(ab)^2 + 4ab(a^2+b^2)
You made a typo in the first line, otherwise fine. You have now reduced the problem to finding a^2+b^2, which you can do using the same method (consider (a+b)^2).
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