How to find the coefficient of $x^2y^3z^6$ in the expression $(x+y+xz)^{4}(y+z)^3$?

Question

I know this is the binomial theorm but not too sure on how to progress. The $(y+z)^3$ and $xz$ is throwing me off as I've not done such a complicated one, but rather just with one expression bracket.

Do I multiply $(x+y+xz)^{4}(y+z)^3$ to form one big expression?

Answer 1

Summing the degrees we get $2+3+6 = 11$

All the terms of $(y+z)^3$ are of combined degree $3.$

That means we need a degree $8$ term from $(x+y+xz)^4$ and the only term of degree $8$ is $(xz)^4$

But then there would be a $x^4$ factor on the other side, which there isn't.

There is no $x^2y^3z^6$ term.