Problem
ALG-B2-M06-P012 Difference for abc times the sum
#12
★★★★☆ Level 4 of 5
Prove that \[a^4+b^4+c^4-abc(a+b+c)=p^4-4p^2q+2q^2+3pr.\]
Hint. Use the previous formula and \(abc(a+b+c)=pr\).
By the previous problem, \(\sum a^4=p^4-4p^2q+2q^2+4pr\). Subtracting \(abc(a+b+c)=pr\), we obtain \(p^4-4p^2q+2q^2+3pr\).
Shows that the expression depends linearly on \(r\), which is a UVW signal.