The given expression is:
34 y^2 + 17 + 3 x^2 +10 y^2 - 10
There are like terms that we can combine before we can decide on the number of terms
the terms in y^2 can be combined giving:
34 y^2 + 10 y^2 = 44 y^2
the numerical terms 17 and -10 we can also combine giving: 17 - 10 = 7
The term in x^2 we cannot combine. So we finally have:
44 y^2 + 3 x^2 + 7
So we started with 5 terms, but they were reduced to 3 terms because the like terms in y^2 and the numerical terms were combined
the coefficients of the initial terms were:
34, 3, 10, 17 , and -10
The variables were y^2, and x^2
The like terms were: 34 y^2 and 10 y^2; and also 17 and -10
The unlike term was : 3 x^2
The final (reduced) expression is: 44 y^2 + 3 x^2 + 7