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A = 232 + ( 223 + 223-224) + (218 - 217 - 217) + ( 29 + 29 - 210) + 1
= 223 + 1
\(A=2^{32}-2^{30}+2^{28}-2^{26}+2^{23}-2^{19}+2^{18}-2^{16}+2^9\)
\(+2^{30}-2^{28}+2^{26}-2^{24}+2^{21}-2^{17}+2^{16}-2^{14}+2^7\)
\(+2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1\)
\(=2^{32}+1\)
Bài này khi nhận thông thường thì ta rút gọn đc hết. :)
a) \(A=85^2-45^2+75^2-35^2+65^2-25^2+55^2-15^2\)
\(A=\left(85-45\right)\left(85+45\right)+....+\left(55-15\right)\left(55+15\right)\)
\(A=40.130+40.110+40.90+40.70\)
\(A=40.\left(130+110+90+70\right)=40.400=16000\)
b) \(B=\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+...+\left(2011-2012\right)\left(2011+2012\right)\)
\(B=-3-7-11-...-4023\)
\(B=-\left(3+7+11+...+4023\right)\)
\(B=-\dfrac{\left(3+4023\right)\left[\dfrac{\left(4023-3\right)}{4}+1\right]}{2}=2025078\)
1: \(=x^3-6x^2+12x-8-8x^3-36x^2-54x-27+7\left(x-1\right)^3\)
\(=-7x^3-42x^2-42x-35+7x^3-21x^2+21x-7\)
\(=-63x^2-21x-42\)
2: \(=x^3+125-\left(x^3-8\right)=125+8=133\)
3: \(=8x^3-27-8x^3-12x^2-6x-1=-12x^2-6x-28\)
Nhân hết ra rồi rút gọn thôi bạn:
\(A=\left(2^9+2^7+1\right)\left(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1\right).\)
\(=2^{32}-2^{30}+2^{28}-2^{26}+2^{23}-2^{19}+2^{18}-2^{16}+2^9\)\(+2^{30}-2^{28}+2^{26}-2^{24}+2^{21}-2^{17}+2^{16}-2^{14}+2^7+2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}\)\(+2^9-2^7+1\)
\(=2^{32}+\left(2^{23}+2^{23}-2^{24}\right)+\left(2^{18}-2^{17}-2^{17}\right)+\left(2^9+2^9-2^{10}\right)+1=2^{32}+1\)
Thanks Witch Rose_ Phù thủy hoa hồng !