Tính nhanh:
a) 8922 + 892 . 216 + 1082
b) 362 + 262 – 52 . 36
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\(a,892^2+216.892+108^2=892^2+2.108.892+108^2=\left(892+108\right)^2=1000^2=1000000\)
b, \(9x^2+42x+49=9.1^2+42.1+49=9+42+49=100\)
c,\(\left(x^2-3x\right)+x-3=x\left(x-3\right)+\left(x-3\right)=\left(x+1\right)\left(x-3\right)=\left(6+1\right)\left(6-3\right)=7. 3=21\)
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) \(2004^2-16=2004^2-4^2=\left(2004-4\right)\left(2004+4\right)=2000.2008=4016000\)
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)\(15,75.175-15,75.55-15,75.20\)\(=15,75.\left(175-55-20\right)\)
\(=15,75.100=1575\)
\(a,2004^2-16=2004^2-4^2=\left(2004-4\right)\left(2004+4\right)=2000.2008=4016000\)\(b,892^2+892.216+108^2=892^2+2.892.108+108^2=\left(892+108\right)^2=1000^2=1000000\)\(c,10,2.9,8-9,8.02+10,2^2-10,2.0,2=9,8\left(10,2-0,2\right)+10,2\left(10,2-0,2\right)=9,8.10+10,2.10=98+102=200\)\(d,36^2+26^2-52.36=36^2-2.36.26+26^2=\left(36-26\right)^2=10^2=100\)\(e,99^3+1+3.\left(99^2+99\right)=99^3+3.99^2+3.99+1^3=\left(99+1\right)^3=100^3=1000000\)
\(f.37.43=\left(40-3\right)\left(40+3\right)=40^2-3^2=1600-9=1591\)
a) \(52^2\)
\(=\left(50+2\right)^2\)
\(=50^2+2\cdot2\cdot50+2^2\)
\(=2500+200+4\)
\(=2704\)
b) \(98^2\)
\(=\left(100-2\right)^2\)
\(=100^2-2\cdot100\cdot2+2^2\)
\(=10000-400+4\)
\(=9604\)
`a, 52^2 = (50+2)^2 = 2500 + 200 + 4 = 2704`
`b, 98^2 = (100-2)^2 = 100^2 - 2 . 100 . 2 + 4 = 10000 - 400 + 4`
`= 9604`
8922 + 892.216 + 1082
= 8922 + 2.892.108 + 1082
= (892 + 108)2
= 10002
= 1000000
a,8922+892.2.108+1082=(892+108)2=10002
b,362+262-2.26.36=(36-26)2=102