Dạng 4: Rút gọn tổng hợp (sử dụng trục căn thức, hằng đẳng thức, phân tích thành nhân tử; …)

A=6+255+1+5−263−2=5+15+1+3−23−2=2

B=35−2+46+2+16+5=35+23+46−24+6−5

=5+2+6−2+6−5=26

C=11+2+12+3+13+4+...+199+100

=2−1+3−2+4−3+...+100−99=9

D=12−3+7−43=12−3+4−43+3=12−3+(2−3)2=12−3+2−3=2+3(2−3)(2+3)+2−3=2+31+2−3=4

E=33−423+1−3+45−23=33−423−1232−1−3+45+2352−232=22−11311−26+13313=2−3−2+3=4−232−4+232=123−12−3+12=123−1−3−1=12.(−2)=−2

F=12+3+26−23+3=12+3+13−233+1=33+1+2+33+1−22+333+12+3=23+433+12+3=23+233+12+3=2.33−133+13−1=233−133−1=33−13=3−33=1−33

A=(3+4)19−83=3+44−32=3+44−3=16−3=13

B=(5)2−22−(2−3)23−2=5−4−2−33−2=1−(−1)=2

C=7+5+7−57+211−3−22

Ta có: 7+5+7−57+2112=14+2447+211=2⇒7+5+7−57+211=2⇒C=2−3−22=2−2−12=2−2+1=1

D=42−52−42+52=222−52−222+52=22−5−22+5=25−2−25+2=25+2−25−25+25−2=25+4−25+45−4=8

E=8−1530−2=115−1.16−2154=115−1.15−12=12

F=3+13−1+3−13+1=3+12+3−123−1=4+23+4−232=4