Question

match each binomial expression with the set of coefficients of the terms obtained by expanding the expression (2x+y)^4, (x+2y)^4, (x+3y)^4, (3x+2y)^4

Answer 1

To solve this we are going to use the fourth row of Pascal's triangle. 
First, we are going to expand our binomials:
$(2x+y)^4=16x^4+32x^3y+24x^2y^2+8xy^3+y^4$

$(x+2y)^4=x^4+8x^3y+24x^2y^2+32xy^3+16y^4$

$(x+3y)^4=x^4+12x^3y+54x^2y^2+108xy^3+81y^4$

$(3x+2y)^4=81x^4+216x^3y+216x^2y^2+96xy^3+16y^4$

We can conclude that you should match each binomial expansion with the set of coefficients of the terms obtained by expanding the expression as follows:
$(2x+y)^4----\ \textgreater \ (16,32,24,8,1)$

$(x+2y)^4----\ \textgreater \ (1,8,24,32,16)$

$(x+3y)^4----\ \textgreater \ (1,12,54,108,81)$

$(3x+2y)^4----\ \textgreater \ (81,216,216,96,16)$