Question

tính nhẩm theo các hằng đẳng thức các số sau:

a,19\(^2\);28\(^2\);81\(^2\);91\(^2\)

b,\(19.21;29.31;39.41\)

c,29\(^2\)-8\(^2\);\(56^2-46^2\);\(67^2-56^2\)

Answer 1

a) \(19^2\)=(20-\(1^2\))=\(20^2\)-2.20.1+\(1^2\)=400-40+1=361;

\(28^2\)=(30-2)\(^2\)=\(30^2\)-2.30.2+2\(^2\)=900-120+4=784;

\(81^2\)=(80+1)\(^2\)=80\(^2\)+2.80.1+1\(^2\)=6400+160+1=6561;

\(91^2\)=(90+1)\(^2\)=90\(^2\)+2.90.1+1\(^2\)=8100+180+1=8281;

b) 19.21=(20-1)(20+1)=20\(^2\)-1=400-1=399;

29.31=(30-1)(30+1)=30\(^2\)-1=900-1=899;

39.41=(40-1)(40+1)=40\(^2\)-1=1600-1=1599

c) \(29^2\)-\(8^2\)=(29-8)(29+8)=21.37=37(20+1)=740+37=777

\(56^2\)-\(46^2\)=(56-46)(56+46)=10.100=1000

\(67^2\)-\(56^2\)=(67-56)(67+56)=11.123=123(10+1)=1230+123=1353

Answer 2

a) =(20-)=-2.20.1+=400-40+1=361;

=(30-2)=-2.30.2+2=900-120+4=784;

=(80+1)=80+2.80.1+1=6400+160+1=6561;

=(90+1)=90+2.90.1+1=8100+180+1=8281;

b) 19.21=(20-1)(20+1)=20-1=400-1=399;

29.31=(30-1)(30+1)=30-1=900-1=899;

39.41=(40-1)(40+1)=40-1=1600-1=1599

c) -=(29-8)(29+8)=21.37=37(20+1)=740+37=777

-=(56-46)(56+46)=10.100=1000