How do I Factor the expression
a y - a^{6} y^{6} ?
ay - a^6 y^6
= ay(1 - a^5 y^5)
Much Ado About Nothing, as Shakespeare would say.
I guess you could go on and make it
ay(1-ay)(1+(ay)+(ay)^2+(ay)^3+(ay)^4)
Not sure that's much better ...
To factor the expression ay - a^6y^6, we can notice that both terms have the factor "a" and "y" in common. Factoring out the greatest common factor, we get:
ay - a^6y^6 = ay(1 - a^5y^5)
So the factored expression is ay(1 - a^5y^5).