Question

tính nhanh

a) \(498^2+996\cdot502+502^2\)b) \(126^2-52\cdot126+26^2\)

c)\(1995^2-1994\cdot1996\)d)\(2005^2-2004\cdot2006\)

e) \(2005^4-2004\cdot2006\cdot\left(2005^2+1\right)\)g) \(1999\cdot\left(2000^2+2001\right)-2001\left(2000^2-1999\right)\)

Answer 1

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Answer 2

a) \(498^2+996.502+502^2\)

\(=498^2+2.498.502+502^2\)

\(=\left(498+502\right)^2\)

\(=1000^2\)

\(=1000000\)

b) \(126^2-52.126+26^2\)

\(=126^2-2.26.126+26^2\)

\(=\left(126-26\right)^2\)

\(=100^2\)

\(=10000\)

Answer 3

c) \(1995^2-1994.1996\)

\(=1995^2-\left(1995-1\right)\left(1995+1\right)\)

\(=1995^2-\left(1995^2-1\right)\)

\(=1995^2-1995^2+1\)

\(=1\)

d) \(2005^2-2004.2006\)

\(=2005^2-\left(2005-1\right)\left(2005+1\right)\)

\(=2005^2-\left(2005^2-1\right)\)

\(=2005^2-2005^2+1\)

\(=1\)

Answer 4

e) \(2005^4-2004.2006\left(2005^2+1\right)\)

\(=2005^4-\left(2005-1\right).\left(2005+1\right)\left(2005^2+1\right)\)

\(=2005^4-\left(2005^2-1\right)\left(2005^2+1\right)\)

\(=2005^4-\left(2005^4-1\right)\)

\(=2005^4-2005^4+1\)

\(=1\)

Answer 5

g) \(1999\left(2000^2+2001\right)-2001\left(2000^2-1999\right)\)

\(=1999.2000^2+1999.2001-2001.2000^2+2001.1999\)

\(=\left(1999.2000^2-2001.2000^2\right)+\left(1999.2001+2001.1999\right)\)

\(=-2.2000+2.2001.1999\)

\(=2\left(1999.2001-2000\right)\)

\(=2.\left(-1\right)=-2\)

Answer 6

\(498^2+996+502^2\)

\(=498^2+2.498.502+502^2\)

\(=\left(498+502\right)^2=1000^2=1000000\)