dùng hàng đẳng thức bình phương tổng 2 số là auto ra, cái chính là tách khéo léo để tạo được thành hàng đẳng thức nhá !!!
a) \(498^2+996.502+502^2\)
\(=498^2+2.498.502+502^2\)
\(=\left(498+502\right)^2\)
\(=1000^2\)
\(=1000000\)
b) \(126^2-52.126+26^2\)
\(=126^2-2.26.126+26^2\)
\(=\left(126-26\right)^2\)
\(=100^2\)
\(=10000\)
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) \(2005^2-2004.2006\)
\(=2005^2-\left(2005-1\right)\left(2005+1\right)\)
\(=2005^2-\left(2005^2-1\right)\)
\(=2005^2-2005^2+1\)
\(=1\)
e) \(2005^4-2004.2006\left(2005^2+1\right)\)
\(=2005^4-\left(2005-1\right).\left(2005+1\right)\left(2005^2+1\right)\)
\(=2005^4-\left(2005^2-1\right)\left(2005^2+1\right)\)
\(=2005^4-\left(2005^4-1\right)\)
\(=2005^4-2005^4+1\)
\(=1\)
g) \(1999\left(2000^2+2001\right)-2001\left(2000^2-1999\right)\)
\(=1999.2000^2+1999.2001-2001.2000^2+2001.1999\)
\(=\left(1999.2000^2-2001.2000^2\right)+\left(1999.2001+2001.1999\right)\)
\(=-2.2000+2.2001.1999\)
\(=2\left(1999.2001-2000\right)\)
\(=2.\left(-1\right)=-2\)
\(498^2+996+502^2\)
\(=498^2+2.498.502+502^2\)
\(=\left(498+502\right)^2=1000^2=1000000\)