(x+h)^3, Im not sure how this works. I feel that I need to f.o.i.l. the problem but I keep getting stuck?

Answer 1

(x + h) (x + h) (x + h)
(x + h) ( x² + 2 h x + h ² )
x ³ + 2 h x ² + h ² x + h x ² + 2 h ² x + h ³
x ³ + (3 h) x ² + (3 h ²) x + h ³

Answer 2

F.O.I.L as normal but when you get the expaned form, you need to go one step further. Here is my solution.

(x+h)*(x+h)*(x+h) (it is the same as (x+h)^3)
FOIL first 2 (x+h)'s as normal.
(x^2+2xh+h^2) but now you have to multiply by another (x+h). from here, just do;
x*(x^2+2xh+h^2)+h*(x^2+2xh+h^2)
then this becomes x^3+3(x^2)h+3xh^2+h^3

or you can do pascal's triangle. Google Pascal's Triangle and it should come up with a triangle of expanded forms when you do binomial expansion

Answer 3

what you do is (x+h)(x+h)(x+h)
so first multiply the first two using foil and you get
(x^2+xh+h^2)
then multiply that to the last (x+h)
You do this by a longer version of foil kind of. First the x to everything and then the h to everything
so you get
x^3+x^2h+xh^2+x^2h+xh^2+h^3
Then simplify it as much as possible
x^3+2x^2h+2xh^2+h^3
I hope this helps!

Answer 4

(x+h)^3=
(x+h)(x+h)(x+h)=
(x^2 + xh + hx + h^2)(x + h)=
(x^2 + 2xh + h^2)(x + h)=
x^3 + 2x^2h +x^2h + x^2h + 2xh^2 + h^3=
x^3 + 2x^2h +2x^2h + 2xh^2 + h^3