Question

Thu gọn

A=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)

Answer 1

+\(\left(a-b\right)\left(a+b\right)=a\left(a+b\right)-b\left(a+b\right)\)

\(=a^2+ab-ab-b^2=a^2-b^2\)

Do đó :\(A=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)+\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)\(A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(A=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(A=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(A=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(A=\left(2^{32}-1\right)\left(2^{32}+1\right)=2^{64}-1\)