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Find $a,b,c,d,e,f,g,h \in \mathbb{R}$ such that

$$ (x+2y+3)(ax+by+cz+d) + (y+z+2)(ex+fy+gz+h) + x+y+z = (ax+by+cz+d)(ex+fy+gz+h)$$

holds in $\mathbb{R}[x,y,z]$.

Is there a $``$good$"$ way for this? Or is there a calculator or afunction in Wolfram Mathematica that can do this automatically?

Any help appreciated!

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  • $\begingroup$ Simplest way, compare coefficients of $x$, $y$ and $z$ and constant terms on both sides and proceed. $\endgroup$ – Akash Patalwanshi Mar 30 at 3:47

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