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I came across this problem and I was not able to think of a way to solve this. I tried to find a pattern by simplifying $(xy+yz+zx)^2$ and then extrapolating the results for the $6^{th}$ power but that also didn't help me. Can someone please tell me how to solve these kinds of problem?

Thanks in advance !!!

Ganit
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  • Look at "multinomial expansions", for instance: here: https://mathonweb.com/help_ebook/html/expressions_8.htm –  Dec 07 '21 at 09:38
  • Previously asked: https://math.stackexchange.com/q/305737/321264. Several similar questions, like https://math.stackexchange.com/q/484908/321264, https://math.stackexchange.com/q/2592558/321264 – StubbornAtom Dec 07 '21 at 13:46

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write the expression in the form: $[y(x+z)+zx]^6$. The term with the 4th power of $y$ is: $$ \binom64 y^4(x+z)^4(zx)^2=\binom64 y^4(x^4+4x^3z +6x^2z^2+4xz^3+z^4)z^2x^2 $$ Thus the coeffecient of $x^3y^4z^5$ is: $$ 4\binom64 $$

am301
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