Problem: The coefficient of x7x^{7}x7 in the polynomial expansion of (1+2x−x2)4\left(1+2x-x^{2}\right)^{4}(1+2x−x2)4 is
Answer Choices:
A. −8-8−8
B. 121212
C. 666
D. −12-12−12
E. none of these Solution:
The coefficient of x7x^{7}x7 in (1+2x−x2)4\left(1+2 x-x^{2}\right)^{4}(1+2x−x2)4 is the coefficient of the sum of four identical terms 2x(−x2)32 x\left(-x^{2}\right)^{3}2x(−x2)3, which sum −8x7-8 x^{7}−8x7.