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\(1.\) 12 x 11 + 21 x 11 x 11 + 11 x 33
= ( 12 x 11 ) + ( 21 x 11 x 11 ) + ( 11 x 33 )
= \(132+2541+363\)
= \(3036\)
132x11-11x32-54x11
= ( 132 x 11 ) - ( 11 x 32 ) - ( 54 x 11 )
\(=1452-352-594\)
= \(506\)
\(2.\)
45 x 32 + 1245
= ( 45 x 32 ) + 1245
= 1400 + 1245
= 2685
75 x 18 + 75 x 21
= ( 75 x 18 ) + ( 75 x 21 )
= 1350 + 1575
= 2925
12 x (27+46) -1567
= 12 x 73 - 1567
= ( 12 x 73 ) - 1567
= 876 - 1567
= - 691
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Đặt \(2000=a\)
\(A=a^9\\ B=\left(a-4\right)\left(a-3\right)\left(a-2\right)\left(a-1\right)a\left(a+1\right)\left(a+2\right)\left(a+3\right)\left(a+4\right)\\ B=\left(a^2-16\right)\left(a^2-9\right)\left(a^2-4\right)\left(a^2-1\right)a< a.a^2.a^2.a^2.a^2=a^9\\ B=\left(a-8\right)\left(a-6\right)\left(a-4\right)\left(a-2\right)a\left(a+2\right)\left(a+4\right)\left(a+6\right)\left(a+8\right)\\ C=\left(a^2-64\right)\left(a^2-36\right)\left(a^2-16\right)\left(a^2-4\right)a\\ C< \left(a^2-9\right)\left(a^2-4\right)\left(a^2-1\right)a< a.a^2.a^2.a^2=a^9\\ D=\left(a-20\right)\left(a-15\right)\left(a-10\right)\left(a-5\right)a\left(a+5\right)\left(a+10\right)\left(a+15\right)\left(a+20\right)\\ D=\left(a^2-400\right)\left(a^2-225\right)\left(a^2-100\right)\left(a^2-25\right)a\\ D< \left(a^2-64\right)\left(a^2-36\right)\left(a^2-16\right)\left(a^2-4\right)a< a.a^2.a^2.a^2=9\)
Vậy \(D< C< B< A\)