Bài giải:
\(x^3-3x^2+3x^2y+3xy^2+y ^3-3y^2-6xy+3x+3y+2012\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(6xy+3x^2+3y^2\right)+\left(3x+3y\right)+2012\)
\(=\left(x+y\right)^3-3\left(2xy+x^2+y^2\right)+3\left(x+y\right)+2012\)
\(=101^3-3.101^2+3.101+2012\)
\(=101^3-3.101^2+3.101-1+2013\)
\(=100^3+2013=1002013\)
Tự kết luận nha bạn ^^
<=>P=(x3+3x2y+3xy2+y3)+(-3x2-3y2)-6xy+(3x+3y)+2012
<=>P=(x+y)3-3(x2+y2)-6xy+3(x+y)+2012
<=>P=(x+y)3-3(x+y)2+6xy-6xy+3(x+y)+2012
<=>P=(x+y)3-3(x+y)2+3(x+y)+2012
<=>P=1013-3.1012+3.101+2012
=>P=1002013