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Input:xy+ 3x2y+ 1 + 2xy2+yx2+ 2 +yx

Intepretation:$xy+3x^2y+1+2xy^2+yx^2+2+yx$

Simplify:

$=3+2xy+4x^2y+2xy^2$

(Function non-further-factorizatable)

$xy + 3x^2y+1+2xy^2+yx^2+2+yx\\ =(xy + yx)+(3x^2y+yx^2)+2xy^2+(1+2)\\ =(xy + xy)+(3x^2y+x^2y)+2xy^2+3\\ =2xy + 4x^2y+2xy^2+3$

Simplify the following expression as far as possible:

xy+ 3x²y+ 1 + 2xy²+yx²+ 2 +yx

$\begin{array}{|rcll|} \hline && xy+ 3x^2y+ 1 + 2xy^2+yx^2+ 2 +yx \\ &=& 3+2xy+ 4x^2y+ 2xy^2 \\ &=& 3+2xy+ 2xy(2x+ y) \\ &=& 3+2xy(1+2x+ y) \\ \hline \end{array}$