<s>[INST] Working out the value of $a^4+b^4$ If $ab = 2$ and $a+b = 5$ then calculate the value of $a^4+b^4$
My approach:
$$a^4+b^4 = (a+b)^4-4a^3b-6a^2b^2-4ab^3$$
$$=(5)^4-6(ab)^2-4ab.a^2-4ab.b^2$$
$$=(5)^4-6(24)-4ab(a^2-b^2)$$
$$=(5)^4-6(24)-8(a+b)(a-b)$$
$$=(5)^4-6(24)-8(5)(a-b)$$
I am a little stuck now and any help will be appreciated.
 [/INST] \begin{align}
a^4+b^4 &= (a+b)^4-4a^3b-6a^2b^2-4ab^3
\\&= (a+b)^{4} - 4 ab (a^{2} + b^{2}) - 6 (ab)^{2}
\\&=
(a+b)^{4} - 4 ab ((a+b)^{2} - 2 ab) - 6 (ab)^{2}
\\&= (a+b)^{4} - 4 ab (a+b)^{2} + 2 (ab)^ {2}.
\end{align}
As noted in a comment, you made a sign error (it happens) in your calculations, otherwise you would have got here yourself.
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