Bài 2:
a) \(\left(a-b-2\right)^2-\left(2a-2b\right)\left(a-b-2\right)+a^2+b^2-2ab\)
\(=\left(a-b-2\right)^2-2\left(a-b\right)\left(a-b-2\right)+\left(a-b\right)^2\)
\(=\left[\left(a-b-2\right)-\left(a-b\right)\right]^2\)
\(=\left(a-b-2-a+b\right)^2\)
\(=\left(-2\right)^2=2^2=4\)
b) \(\left(2+1\right)\left(2^2+1\right)...\left(2^{256}+1\right)-1\)
\(=1\left(2+1\right)\left(2^2+1\right)...\left(2^{256}+1\right)-1\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)...\left(2^{256}+1\right)-1\)
\(=\left(2^2-1\right)\left(2^2+1\right)...\left(2^{256}+1\right)-1\)
\(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{256}+1\right)-1\)
...
\(=\left(2^{256}-1\right)\left(2^{256}+1\right)-1\)
\(=2^{512}-1-1\)
\(=2^{512}-2\)
\(=2\left(2^{511}-1\right)\)
c) \(24\left(5^2+1\right)\left(5^4+1\right)...\left(5^{32}+1\right)-5^{64}\)
\(=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)...\left(5^{32}+1\right)-5^{64}\)
\(=\left(5^4-1\right)\left(5^4+1\right)...\left(5^{32}+1\right)-5^{64}\)
...
\(=\left(5^{32}-1\right)\left(5^{32}+1\right)-5^{64}\)
\(=5^{64}-1-5^{64}\)
\(=-1\)
Chúc bạn học tốt!
