Question

[Phạm Nguyễn Khánh Huyền]

tính nhanh giá trị biểu thức

1. 33²+83²-66x87
2. 45²+40²-10²+80x45
3. 3x(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

Answer 1

[Teen]

\(45^2+40^2-10^2+80.45\)

\(=\left(45+40\right)^2-10^2\)

\(=\left(45+40-10\right)\left(45+40+10\right)\)

\(=75.95=7125\)

Answer 2

[Teen]

\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

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

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

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

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

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