Problem: If 21998−21997−21996+21995=k⋅219952^{1998}-2^{1997}-2^{1996}+2^{1995}=k \cdot 2^{1995}21998−21997−21996+21995=k⋅21995, what is the value of k?k?k?
Answer Choices:
A. 111
B. 222
C. 333
D. 444
E. 555
Solution:
Factor the left side of the given equation:
21998−21997−21996+21995=(23−22−2+1)21995=3⋅21995=k⋅219952^{1998}-2^{1997}-2^{1996}+2^{1995}=\left(2^{3}-2^{2}-2+1\right) 2^{1995}=3 \cdot 2^{1995}=k \cdot 2^{1995} 21998−21997−21996+21995=(23−22−2+1)21995=3⋅21995=k⋅21995
so k=3k=3k=3.