Question

expand (1+y+y²)⁴. by binomial theorem

Answer 1

let y+y²=t

then (1+t)⁴= 1 + 4t + 6t² + 4t³+ t⁴

t=y(1+y)
t²=y²(1+2y+y²)
t³=y³(1+3y+3y²+y³)
t⁴=y⁴(1+4y+6y²+4y³+y⁴)

put the values to get the answer.

you could use multinomial theorm for simplicity.