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\(a,=27\cdot20+73\cdot20-27=20\left(27+73\right)-27\\ =20\cdot100-27=2000-27=1973\\ b,=42\cdot50-38\cdot50-50\cdot2=50\left(42-38-2\right)=50\cdot2=100\\ e,=254\left(58+21\cdot2\right)=254\cdot100=25400\\ c,=53\left(12+172-84\right)=53\cdot100=5300\\ d,=24\left(31+42+27\right)=24\cdot100=2400\\ f,=\left(9-8-...-1\right)\left(500\cdot9-500\cdot9\right)=\left(9-8-...-1\right)\cdot0=0\)
\(A=\left(-1\right)+2-3+\left(-4\right)+5-6+\left(-7\right)+8-9\)
\(=2-1-3+5-4-6+8-7-9\)
\(=\left(2-1-3\right)+\left(5-4-6\right)+\left(8-7-9\right)\)
\(=\left(-2\right)+\left(-5\right)+\left(-8\right)\)
\(=-15\)
\(=\left(9-8-...-2-1\right)\left(500\cdot9-500\cdot9\right)=0\)
a) 815 – 23 – 77 +185 = (815 + 185) – (23+77) = 1000 – 100 = 900
b) 3145 – 246 + 2347 – 145 + 4246 – 347
= (3145-145) + (4246 – 246) + (2347 – 347)
= 3000 + 4000 + 2000 = 9000
c) (2018:1 – 2018.1):(2018.2008+2018.2002) = 0 : (2018.2008+2018.2002) = 0
d) (9 – 8 – 7 – 6 – … – 2 – 1).(500.9 – 250.18)
= (9 – 8 – 7 – 6 – … – 2 – 1).(500.9 – 250.2.9)
= (9 – 8 – 7 – 6 – … – 2 – 1).(500.9 – 500.9)
= (9 – 8 – 7 – 6 – … – 2 – 1).0 = 0
\(B=2+2^2+2^3+2^4+...+2^{99}+2^{100}=2\left(1+2^2+2^3+2^4\right)+...+2^{96}\left(1+2^2+2^3+2^4\right)=2.31+2^6.31+...+2^{96}.31=31\left(2+2^6+...+2^{96}\right)⋮31\)
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