Question

How do you use the binomial series to expand `(1 + 3x) ^8`?

Answer 1

Pascal's triangle.

Explanation:

Since you're taking the binomial to the 8th power you would use the 8th row of this triangle and say that

`1(1)(3x)+8(1)(3)x+28(1)(3x)+56(1)(3x)+70(1)(3x)+56(1)(3x)+28(1)(3x)+8(1)(3x)+1(1)(3x)`

and then add your exponents in a descending order so

`1(1)^8(3x)^0+8(1)^7(3x)^1+28(1)^6(3x)^2+56(1)^5(3x)^3+70(1)^4(3x)^4+56(1)^3(3x)^5+28(1)^2(3x)^6+8(1)^1(3x)^7+1(1)^0(3x)^8`

and simplify.