a. \(37,5\cdot6,5-7,5\cdot3,4-6,6\cdot7,5+3,5\cdot37,5=\left(37,5\cdot6,5+3,5\cdot37,5\right)-\left(7,5\cdot3,4+6,6\cdot7,5\right)=37,5\left(6,5+3,5\right)-7,5\left(3,4+6,6\right)=37,5\cdot10-7,5\cdot10=375-75=300\)

b. \(45^2+40^2-15^2+80\cdot45=45^2+2\cdot40\cdot45+40^2-15^2=\left(45+40\right)^2-15^2=85^2-15^2=\left(85-15\right)\left(85+15\right)=70\cdot100=7000\)

b. Ta có: \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2^8-1\right)\left(2^8+1\right)=2^{16}-1< 2^{16}\)

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