8:
a: \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)
b: \(100^2+103^2+105^2+94^2-101^2-98^2-96^2-107^2\)
\(=\left(100-107\right)\left(100+107\right)+\left(103-96\right)\left(103+96\right)+\left(105-98\right)\left(105+98\right)+\left(94-101\right)\left(94+101\right)\)
\(=-7\cdot\left(100+107\right)+7\cdot\left(103+96\right)+7\cdot\left(105+98\right)+\left(-7\right)\cdot\left(94+101\right)\)
\(=7\left(-100-107+103+96+105+98-94-101\right)\)
=0
=>\(100^2+103^2+105^2+94^2=101^2+98^2+96^2+107^2\)
Bài 10:
\(2\left(a^2+b^2\right)=\left(a-b\right)^2\)
=>\(2a^2+2b^2=a^2-2ab+b^2\)
=>\(a^2+2ab+b^2=0\)
=>\(\left(a+b\right)^2=0\)
=>a+b=0
=>a và b là hai số đối nhau
