If n is the degree of the polynomial, [5x3+1−5x3−1]−8+[5x3+1+5x3−1]−8 and m is the coefficient of xn in it, then the ordered pair (n,m) is equal to:
Solutions · 1
Official solution
Rationalizing and combining (as derived in the source, using (a+b)4+(a−b)4-type binomial expansion with a=5x3+1,b=5x3−1 after simplification):
\[\text{Expression}=\frac{1}{2^8}\left[8C_0(5x^3+1)^4+8C_2(5x^3+1)^3(5x^3-1)+\cdots+8C_8(5x^3-1)^4\right]\]
Degree of the resulting polynomial is n=12, and the coefficient of x12 works out to
\[m=5^4\times\frac{2^8}{2^8}\times2^3=8(10)^4\]
\[(n,m)=(12,\,8(10)^4)\]