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\(=9,8\left(10,2-0,2\right)+10,22-2,04\)
=98+10,22-2,04
=106,18
\(=9,8\cdot10+10,2^2-10,2\cdot0,2\)
=98+104,04-2,04
=198
\(=10,2\left(9,8+10,2-0,2\right)-9,8\cdot0,2\)
\(=10,2\cdot19,8-9,8\cdot0,2\)
=201,96-1,96=200
a: \(2004^2-16\)
\(=\left(2004-4\right)\left(2004+4\right)=2000\cdot2008=4016000\)
b: \(892^2+892\cdot216+108^2\)
\(=892^2+2\cdot892\cdot108+108^2\)
\(=\left(892+108\right)^2=1000^2=1000000\)
c: \(36^2+26^2-52\cdot36\)
\(=36^2-2\cdot36\cdot26+26^2\)
\(=\left(36-26\right)^2=10^2=100\)
d: \(\left(10,2\cdot9,8-9,8\cdot0,2\right)+\left(10,22-10,2\cdot0,2\right)\)
\(=9,8\left(10,2-0,2\right)+10,22-2,04\)
=98+8,18
=106,18
e: \(20,03\cdot45+20,03\cdot47+20,03\cdot8\)
\(=20,03\cdot\left(45+47+8\right)\)
\(=20,03\cdot100=2003\)
g: \(15,75\cdot175-15,75\cdot55-15,75\cdot20\)
\(=15,75\cdot\left(175-55-20\right)\)
\(=15,75\cdot100=1575\)
h: \(A=57^2+114\cdot43+43^2\)
\(=57^2+2\cdot57\cdot43+43^2\)
\(=\left(57+43\right)^2=100^2=10000\)
i: \(B=5^4\cdot3^4-\left(15^2-1\right)\left(15^2+1\right)\)
\(=15^4-\left(15^4-1\right)=1\)
k: \(C=50^2-49^2+48^2-47^2+\cdots+2^2-1^2\)
\(=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+\cdots+\left(2-1\right)\left(2+1\right)\)
=50+49+...+2+1
\(=50\cdot\frac{51}{2}=25\cdot51=1225\)
a: \(2004^2-16=2000\cdot2008=4016000\)
b: \(892^2+892\cdot216+108^2=1000^2=1000000\)
c: \(36^2-52\cdot36+26^2=10^2=100\)
10,2.9,8-9,8.0,2+10,22-10,2.0,2
=9,8(10,2-0,2)+10,2.10,2-10,2.0,2
= 9,8.10+10,2.(10,2-0,2)
= 98+10,2.10
=98+102
=200
\(=9,8\cdot10+10,22-2,04=106,18\)