rút gọn (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1) 23/09/2021 Bởi Camila rút gọn (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)
Đáp án: $${2^{32}} – 1$$ Giải thích các bước giải: $$\eqalign{ & \left( {2 + 1} \right)\left( {{2^2} + 1} \right)\left( {{2^4} + 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr & = \left( {{2^2} – 1} \right)\left( {{2^2} + 1} \right)\left( {{2^4} + 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr & = \left( {{2^4} – 1} \right)\left( {{2^4} + 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr & = \left( {{2^8} – 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr & = \left( {{2^{16}} – 1} \right)\left( {{2^{16}} + 1} \right) = {2^{32}} – 1 \cr} $$ Bình luận
Đáp án:
$${2^{32}} – 1$$
Giải thích các bước giải:
$$\eqalign{
& \left( {2 + 1} \right)\left( {{2^2} + 1} \right)\left( {{2^4} + 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr
& = \left( {{2^2} – 1} \right)\left( {{2^2} + 1} \right)\left( {{2^4} + 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr
& = \left( {{2^4} – 1} \right)\left( {{2^4} + 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr
& = \left( {{2^8} – 1} \right)\left( {{2^8} + 1} \right)\left( {{2^{16}} + 1} \right) \cr
& = \left( {{2^{16}} – 1} \right)\left( {{2^{16}} + 1} \right) = {2^{32}} – 1 \cr} $$