<s>[INST] Help with sum of coefficients please! Problem 1: "Imagine that the polynomial $(1 + x - y)^3$ is converted to the standard form. What is the sum of its coefficients?"
Problem 2 (continued): "What is the sum of the coefficients of the terms not containing $y$?"
Problem 3 (continued): "What is the sum of the coefficients of the terms containing $x$?"
I'm able to solve problem 1 & 2, but I've been stuck on 3 for hours..I'd really appreciate it if someone could explain how to solve it :D
 [/INST] One should expand $(1+x-y)^3$ as follows  $$(1+x-y)^3$$$$=(1+x-y)(1+x-y)^2$$
$$=(1+x-y)(1+x^2+y^2+2x-2xy-2y)$$
$$=1+x^2+y^2+2x-2xy-2y+x(1+x^2+y^2+2x-2xy-2y)-y(1+x^2+y^2+2x-2xy-2y)$$
$$=1+x^2+y^2+2x-2xy-2y+x+x^3+xy^2+2x^2-2x^2y-2xy-y-x^2y-y^3-2xy+2xy^2+2y^2$$
$$=\color{red}{x^3-y^3-3x^2y+3xy^2+3x^2+3y^2-6xy+3x-3y+1}$$
I hope you can take it from here 
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