Expansion using Pascal's triangle

Question

I want to expand $(3k+1)^3$. When doing this I got $27k^3+9k^2+3k+1$ but when I expanded the expression by foiling I got $27k^3+9k^2+27k+1$. Which one is correct?

Answer 1

You have $(3k+1)^3=(3k)^3+3(3k)^2(1)+3(3k)(1)^2+1^3$, so see what this gives when you simplify.

Answer 2

$$(3k+1)^3$$ The third row of Pascal's Triangle is $1,3,3,1$. THus, these are the coefficients of each term in the expansion. Now you apply the powers in descending order for the first term, and ascending order for the second term. THen $$(3k+1)^3=1\cdot (3k)^3\cdot 1^0+3\cdot (3k)^2\cdot 1^1+3\cdot (3k)^1\cdot1^2+1\cdot (3k)^0\cdot1^3$$ $$=27k^3+27k^2+9k+1$$