# Thread: Pascals triangle...?

1. ## Pascals triangle...?

hey, this is my problem:

Expand (a+b)^0, (a+b)^1, (a+b)^2, etc

(a+b)^0 = 1
(a+b)^1 = a + b
(a+b)^2 = a^2 + 2ab + b^2
(a+b)^3 = a^3 + 3a^(2)b + 3a(b^2) + b^3
(a+b)^4 = a^4 + 4(a^3)b + 6(a^2)(b^2) + b^4

I can see how this relates to pascals triangle, im just having a bit of trouble with a couple of questions about this...

What is the sum of the powers in each term of (a+b)^n?

all i can really think of is (a+b)^n = a^n + a^(n-1)... but im not sure what comes after this.

honestly i have no idea, but i think its something like that ^

Or i could be completely wrong. anyway, any help would be appreciated! thanks.

2. Hi

Let's do it for $\displaystyle n=2$ : $\displaystyle (a+b)^2=a^2+2ab+b^2$
• first term : $\displaystyle a^2=a^2b^0$ : the sum of the powers is $\displaystyle 2+0=2$
• second term : $\displaystyle 2ab=2a^1b^1$ : the sum of the powers is $\displaystyle 1+1=2$
• third term : same idea as in the case of the first one. The result is $\displaystyle 2$.
Hope that helps.

3. yes, that was helpful. thanks