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a: \(36^2+26^2-52\cdot36=\left(36-26\right)^2=10^2=100\)
b: \(99^3+1+3\left(99^2+99\right)\)
\(=\left(99+1\right)^3-3\cdot99\cdot1\cdot\left(99+1\right)+3\left(99^2+99\right)\)
=100^3=10^6
a) \(2004^2-16=2004^2-4^2=\left(2004-4\right)\left(2004+4\right)=2000.2008=4016000\)
b) \(892^2+892.216+108^2\)\(=892^2+2.892.108+108^2\)
\(=\left(892+108\right)^2\)
\(=1000^2=1000000\)
c) \(10,2.9,8-9,8.0,2+10,2^2-10,2.0,2\)\(=9,8\left(10,2-0,2\right)+10,2\left(10,2-0,2\right)\)
\(=9,8.10+10,2.10\)
\(=98+102=200\)
d) \(36^2+26^2-52.36=36^2-2.36.26+26^2\)
\(=\left(36-26\right)^2=10^2=100\)
g) \(20,03.45+20,03.47+20,03.8\)\(=20,03.\left(45+47+8\right)\)
\(=20,03.100=2003\)
h)\(15,75.175-15,75.55-15,75.20\)\(=15,75.\left(175-55-20\right)\)
\(=15,75.100=1575\)
a: \(2004^2-16=2000\cdot2008=4016000\)
b: \(892^2+892\cdot216+108^2=1000^2=1000000\)
c: \(36^2-52\cdot36+26^2=10^2=100\)
a) 20042 - 16
= 20042 - 42
= (2004 - 4)(2004 + 4)
= 2000.2008
= 4016000
b) 10,2.9,8 - 9,8.0,2 + 10,2.0,2
= 9,8(10,2 - 0,2) + 2,04
= 9,8.10 + 2,04
= 98 + 2,04
= 100,04
Câu 3:
a, Ta có: \(n^2\left(n+1\right)+2n\left(n+1\right)\)
\(=\left(n^2+2n\right)\left(n+1\right)=n\left(n+1\right)\left(n+2\right)⋮6\forall n\in Z\) ( do tích của 3 số liên tiếp chia hết cho 6 )
\(\Rightarrowđpcm\)
b, \(\left(2n-1\right)^3-\left(2n-1\right)\)
\(=\left(2n-1\right)\left[\left(2n-1\right)^2-1\right]\)
\(=\left(2n-1\right)\left(2n-1-1\right)\left(2n-1+1\right)\)
\(=\left(2n-1\right)\left(2n-2\right)2n⋮8\forall n\in Z\)
\(\Rightarrowđpcm\)
a) 20042 - 16
= 20042 - 42
= (2004 - 4)(2004 + 4)
= 2000.2008
= 4016000
b) 8922 + 892.216 + 1082
= 8922 + 2.892.108 + 1082
= (892 + 108)2
= 10002
= 1000000
c) 10,2.9,8 - 9,8.0,2 + 10,2.0,2
= 9,8(10,2 - 0,2) + 2,04
= 9,8.10 + 2,04
= 98 + 2,04
= 100,04
d) 362 + 262 - 52.36
= 362 - 2.36.26 + 262
= (36 - 26)2
= 102
= 100
\(A=2004^2-16=\left(2004-4\right)\left(2004+4\right)=2000\cdot2008=4016000\)
\(B=892^2+892\cdot216+108^2=892^2+2\cdot892\cdot108+108^2=\left(892+108\right)^2=1000^2=1000000\)
\(C=10,2\cdot9,8-9,8\cdot0,2+10,2^2-10,2\cdot0,2\)
\(=9,8\left(10,2-0,2\right)+10,2\left(10,2-0,2\right)\)
\(=10\cdot\left(9,8+10,2\right)=10\cdot20=200\)
\(D=36^2+26^2-52\cdot36=\left(36-26\right)^2=10^2=100\)
\(E=105^2-25=\left(105-5\right)\left(105+5\right)=100\cdot110=11000\)
\(F=73^2-27^2=\left(73-27\right)\left(73+27\right)=46\cdot100=4600\)
A. 20042-16=20042-42=(2004-4)(2004+4)=2000.2008=2016000
B. 8922+892.216+1082= 8922+2.892.108+1082=(892+108)2=10002=1000000
C.Khó nhìn quá
D.362+262-52.36=362-2.36.26+262=(36-16)2=202=400
E.1052-25=(105-5)(105+5)=100.110=11000
F. 732-272=(73-27)(73+27)=46.100=4600
a) 20042 - 16
= (2004-4) (2004+4) = 2000.2008 = 4016000
b) 362 + 262 - 52.36
= (36-26)2 = 102 = 100
c) 37.43
Có: AB.CD = A.C, A.D+B.C, B.D ( tính từ dưới lên, phép tính có nhớ)
⇒ 37.43 = 1591
d) 20,03.45 + 20,03. 47 + 20,03.8
= 20,03. ( 45+47+8) = 20,03. 100 = 2003