Lời giải:
Với $x=-1\Rightarrow x+1=0$. Do đó:
$A=(x^{2014}+x^{2013})+(x^{2012}+x^{2011})+...+(x^2+x)+1$
$=x^{2013}(x+1)+x^{2011}(x+1)+...+x(x+1)+1$
$=x^{2013}.0+x^{2011}.0+...+x.0+1=1$
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\(x=-1; y=1\Rightarrow xy+1=0\)
\(B=(x^{100}y^{100}+x^{99}y^{99})+...+(x^2y^2+xy)+1\)
\(=x^{99}y^{99}(xy+1)+...+xy(xy+1)+1\)
\(=x^{99}y^{99}.0+....+xy.0+1=1\)