Lời giải:
a. $=(36+76)-89-(44+56)$

$=112-89-100=12-89=-(89-12)=-77$
b. $=342-567-642+767-458$

$=(342-642)+(767-567)-458=-300+200-458=-100-458=-(100+458)=-558$

c. $=1892-892+852-300-852$

$=(1892-892)+(852-852)-300=1000+0-300=700$

d.

$=472-281-513-372+181-487$

$=(472-372)-(281-181)-(513+487)$

$=100-100-1000=-1000$

e.

$=912-1268-812+1368-100$

$=(912-812)+(1368-1268)-100=100+100-100=100$

a) ( 100   –   1 ) 3  = 970299.                          b) ( 91   +   9 ) 3   =   100 3 .

c) ( 1000   +   1 ) 3  = 1003003001.                d) ( 102   –   2 ) 3   =   100 3 .

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: \(36^2-52\cdot36+26^2=10^2=100\)

\(M=896+892+888+...+24\)

\(M=\frac{\left(896+24\right).219}{2}=100740\)

\(N=18.21+21+21.79\)

\(N=21.\left(18+1+79\right)=21.100\)

\(N=2100\)

b,

N=18x21+21+21x79

N=18x21+21x1+21x79

N=(18+1+79)x21

N=98x21

N=2058

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

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

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

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

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

a) = (892+108)²

=100²

=1000000

b)=(36-26)²

=10²

=100