giúp mik bài 5 vs mấy bạn eiiiiiiiii

Đáp án:

Giải thích các bước giải:

 a) \({101^2};\) 

\(\eqalign{
& {101^2} = {\left( {100 + 1} \right)^2} \cr 
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {100^2} + 2.100.1 + {1^2} \cr 
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 10000 + 200 + 1 \cr 
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 10201 \cr} \)

\({199^2};\) 

\(\eqalign{
& {199^2} = {\left( {200 - 1} \right)^2} \cr 
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {200^2} - 2.200.1 + {1^2} \cr 
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 40000 - 400 + 1 = 39601 \cr} \)

b) `37.43=(40-3)(40+3)=(40)^2-3^2=1600-9=1591`

 `39.41=(40-1)(40+1)=1600-1=1599`

c) `67^2-33^2=(67-33)(67+33)=34.100=3400`

d) `2011^2-2010.2012`

`=2011.(2010+1)-2010.2012`

`=2010.2011-2010.2012+2011`

`=2010.(2011-2012)+2011`

`=-2010+2011=1`

e) `2006^2-2005^2+2004^2-2003^2+...+2^2-1^2`

`=(2006+2005)(2006-2005)+(2004+2003)(2004-2003)+............+(2+1)(2-1)`

`=(2006+2005).1+(2004+2003).1+..........+(2+1).1`

`=2006+2005+2004+2003+...........+2+1`

`=1+2+3+4+...........+2004+2005+2006`

`=(1+2006).2006:2=2013021`

f)

\(85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)

\(=\left(85^2-15^2\right)+\left(75^2-25^2\right)+\left(65^2-35^2\right)+\left(55^2-45^2\right)\)

\(=\left(85-15\right)\left(85+15\right)+\left(75-25\right)\left(75+25\right)+\left(65-35\right)\left(65+35\right)+\left(55-45\right)\left(55+45\right)\)

\(=70.100+50.100+30.100+10.100\)

\(=7000+5000+3000+1000\)

\(=16000\)