Question

Thu gọn các biểu thức sau:
a) \(A=2^{n-1}+2.2^{n+3}-8.2^{n-4}-16.2^n\)

b) \(B=\left(3^{n+1}-2.2^n\right)\left(3^{n+1}+2.2^n\right)-3^{2n+2}+\left(8.2^{n-2}\right)^2\)

Answer 1

a) \(A=2^{n-1}+2.2^{n+3}-8.2^{n-4}-16.2^n\)

\(=2^{n-1}+2^{n+3+1}-2^{n-4+3}-2^{n+4}\)

\(=2^{n-1}+2^{n+4}-2^{n-1}-2^{n+4}\)

\(=0\)

b) \(B=\left(3^{n+1}-2.2^n\right)\left(3^{n+1}+2.2^n\right)-3^{2n+2}+\left(8.2^{n-2}\right)^2\)

\(=\left(3^{n+1}-2^{n+1}\right)\left(3^{n+1}-2^{n+1}\right)-3^{2n+2}+2^{2n+2}\)

\(=3^{2n+2}-2^{2n+2}-3^{2n+2}+2^{2n+2}\)

\(=0\)