a)
143^2-43^2=(100+43)^2-43^2=10000+8600+43^2-43^2=18600
b)
1959^2-41^2=(2000-41)^2-41^2=4000000-82000+41^2-41^2=3918000
c)
1003*997=(1000+3)(1000-3)=1000000-9=999991
d)
302*298=(300+2)(300-2)=90000-4=89996
e)
\frac{49^2-41^2}{54^2-46^2}=\frac{(50-1)^2-(40+1)^2}{(50+4)^2-(50-4)^2}=\frac{2500-100+1-(1600+80+1)}{50^2+400+16-(50^2-400+16)}=
=\frac{2400+1-1680-1}{50^2+400+16-50^2+400-16}=\frac{720}{800}=\frac{9}{10}=0,9
f)
\frac{66^2-54^2}{75^2-45^2}=\frac{60^2+720+36-(60^2-720+36)}{60^2+1800+15^2-(60^2-1800+15^2)}=
=\frac{60^2+720+36-60^2+720-36}{60^2+1800+15^2-60^2+1800-15^2}=
=\frac{1440}{3600}=\frac{4}{10}=0,4