892^2 =892*892

=>892*892+892+1

892*[892+1]

892*893=796556

796556

892² + 892.216 + 108²

= 892² + 2.892.108 + 108²

= (892 + 108)²

= 1000²

= 1000000

1000000

\(\frac{400}{101}\)

\(A=\frac{113+892+187+808}{742-23+158-372}\)

\(A=\frac{\left(113+187\right)+\left(892+808\right)}{\left(742-372\right)+\left(158-23\right)}\)

\(A=\frac{300+1700}{370+135}\)

\(A=\frac{2000}{505}=\frac{400}{101}\)

202676

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: \(36^2-52\cdot36+26^2=10^2=100\)

-52.112+112-(112).(-47)

=112(-52+1-(47))

=112.(-98)

=-10976

b)\(892^2+892.216+108^2=892^2+2.892.108+108^2\\ =\left(892+108\right)^2=1000^2=1000000\)

c)\(10,2.9,8-9,8.0,2+10,2^2-10,2.0,2=9,8.\left(10,2-0,2\right)+10,2.\left(10,2-0.2\right)\\ =9,8.10+10,2.10=98+102=200\)