Problem: If (3x−1)7=a7x7+a6x6+…+a0(3 x-1)^{7}=a_{7} x^{7}+a_{6} x^{6}+\ldots+a_{0}(3x−1)7=a7x7+a6x6+…+a0, then a7+a6+…+a0a_{7}+a_{6}+\ldots+a_{0}a7+a6+…+a0 equals
Answer Choices:
A. 000
B. 111
C. 646464
D. −64-64−64
E. 128128128 Solution:
The sum of the coefficients of a polynomial p(x)p(x)p(x) is equal to p(1)p(1)p(1); (3⋅1−1)7=128(3 \cdot 1-1)^{7}=128(3⋅1−1)7=128.