Question

How do you use the binomial series to expand `(x + 3)^6`?

Answer 1

`x^6 + 18x^5 + 135x^4 + 540x^3 + 1215x^2 + 1458x +729`

Explanation:

The binomial series gives you :
`(a+b)^6 = a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 +b^6`

Substitute a and b by x and 3 and you get:

`(x+3)^6 = x^6 + 18x^5 + 135x^4 + 540x^3 + 1215x^2 + 1458x +729`