How do you expand (x+h)^3 ?
I’ll assume you don’t know the binomial theorem. So instead, let’s just consider what
Well, remember how to “FOIL”? FOILing means that when you multiply TWO binomials, you multiply the First of each binomial together plus the Outer two plus the Inner two and finally add the Last two. I.e.
( a + b ) ( c + d ) = ac + ad + bc + bd
We can use this to figure out our cube of a binomial. But first let’s figure out what the square of a binomial is using the FOIL method:
Now we just multiply this trinomial by the last binomial to get the final result. Note that this isn’t exactly FOIL, but hopefully it’s clear that we’re just multiplying each term in the first polynomial by each term in the second and adding:
And thus we find our result.