\(A=3\left(x^2+y^2\right)-2\left(x^3+y^3\right)\)
\(=3x^2+3y^2-2\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=3x^2+3y^2-2.1\left(x^2-xy+y^2\right)\)
\(=3x^2+3y^2-2x^2+2xy-2y^2\)
\(=x^2+2xy+y^2=\left(x+y\right)^2=1^2=1\)
\(B=x^3+y^3+3xy\left(x^2+y^2\right)+6x^2y^2\left(x+y\right)\)
\(=x^3+y^3+3xy\left[\left(x+y\right)^2-2xy\right]+6x^2y^2.1\)
\(=x^3+y^3+3xy\left(x+y\right)^2-6x^2y^2+6x^2y^2\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\)
\(=x^2-xy+y^2+3xy\)
\(=x^2+2xy+y^2=\left(x+y\right)^2=1^2=1\)