a)
41+{1+[4⋅(1+3−1)−1]−1}−1=41+⎩⎨⎧1+[4⋅(1+31)−1]−1⎭⎬⎫−1=
=41+⎩⎨⎧1+[4⋅(34)−1]−1⎭⎬⎫−1=41+{1+[4⋅43]−1}−1=
=41+{1+3−1}−1=41+{1+31}−1=41+{34}−1=41+43=1
b)
49⋅39−23⋅273−2⋅8143⋅(91)−1=342⋅3(32)−23⋅3233−2⋅(34)43⋅(3−2)−1=
=321⋅33−3⋅3233−2⋅33⋅32=321⋅3−33⋅3233−2+3+2=
=321−1+2333=3133=32=9
c)
5−3⋅325−235−2⋅125−32⋅(51)2=5−3⋅3(52)−235−2⋅(53)−32⋅(5−1)2=
=5−3⋅35−35−2⋅5−2⋅5−2=5−3⋅5−335−2−2−2=5−3−15−6=5−45−6=
=5−6−(−4)=5−6+4=5−2=(51)2=251
d)
545−420−50025−10=59⋅5−44⋅5−100⋅525−10=
=5⋅35−4⋅25−10525−10=155−85−10525−10=
=−3525−10=−3525−10⋅55=−1510−105=
=−1510(1−5)=−32(1−5)=32(5−1)
e)
(7+37+5)2−(7−5)2= >07+37+5−<07−5 =
=7+37+5−(−7+5)=7+37+5+7−5=
=7+37+5+7+3(7−5)(7+3)=7+37+5+7+37+37−57−15=
=7+37+5+7+37−57−15=7+3−7−3=7+3−(7+3)=∣−1∣=1
f)
31−483−76−73−54−3−16−3−41=3−383−7−13−27⋅2−3−8⋅2−3−41=
=3−827+1−332+232+341=−23+1−32+341=−21−32+341=
=2(32−341)=2(348−341)=2⋅341⋅(38−31)=
=2⋅341⋅(2−1)=2341=38⋅341=348=32
