# Foil (u+3) ^3............?

Im having a brainfart...what is the foil of (u+3) ^3

Relevance

firstly

you should expand that (u+3)^3 into

(u+3)(u+3)(u+3)

*remember that foil means first, outer, inner, last

and after that multiply two terms out using foil method

(u+3)(u+3)

u^2 +3u +3u + 9

combine like terms

u^2 +6u + 9

and finally multiply this by the remaining (u+3) using foil method

(u^2 + 6u + 9)(u+3)

u^3 +3u^2 +6u^2 + 18u + 9u + 27

combine like terms

u^3 + 9u^2 + 27u + 27

Source(s): an honours math student

I will show you two methods, first with foil, then with the binomial theorem.

FOIL

(u + 3)^3 = (u + 3)*(u + 3)*(u + 3)

= (u^2 + 3u + 3u + 9)*(u + 3)

= (u^2 + 6u + 9)*(u + 3)

= (u^3 + 3u^2 + 6u^2 + 18u + 9u + 27)

= u^3 + 9u^2 + 27u + 27

Binomial Theorem

First, the third row in pascal's triangle is 1, 3, 3, 1. These are used for the binomial theorem.

(u + 3)^3 = 1*(u)^3*(3)^0 + 3*(u)^2*(3)^1 + 3*(u)^1*(3)^2 + 1*(u)^0*(3)^3

= u^3 + 9u^2 + 27u + 27

Personally, I prefer the binomial theorem, but it's all up to you.

Hope that helped =D

Just do it one step at a time. (u+3)x(u+3) =u^2+3u+3u+9 which simplifies to u^2+6u+9

(u^2+6u+9)(u+3) is u^3+6u^2+9u+3u^2+18u+27

simplify this combining your numbers according to like terms (with same power) and you get your final answer-

u^3+9u^2+27u+27

(u + 3) (u + 3) (u + 3)

(u^2 + 6u +9) (u + 3)

u^3 + 3u^2 + 6u^2 + 18u + 9u +27

u^3 + 9u^2 + 27u +27

yay. math.