Question 853104
Express the numerator as {{{y^4+0*y^3+0*y^2+0*y+a^2}}}.  That is like expanded form for powers of y.  Everything else is just the same as you would do for long division of decimal numbers.  Expect, for your example, a few very lengthy, messy steps within the process.



y+a_____|___y^3__________________________________This is the quotient line(unfinished)
________|______________________________________
________|___y^4___0*y^3____0*y^2____0*y_____a^2
____________y^4___ay^3
________________________
_____________0___-ay^3



Next, ask yourself, how many times does y go into {{{-ay^3}}}?...


Much easier to do all of this process on paper than to try to type in so much text.



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Just to take the process two more partial quotients,


y+a_____|___y^3___-ay^2____a^2*y________________________This is the quotient line(unfinished)
________|______________________________________
________|___y^4___0*y^3____0*y^2____0*y_____a^2
____________y^4___ay^3
________________________
_____________0___-ay^3____
_________________-ay^3____-a^2y^2
__________________________________
_________________0________a^2y^2
__________________________a^2y^2___a^3*y