Question

How do you use the Binomial Theorem to expand `(2x+1)^4`?

Answer 1

`(2x+1)^4 = 16x^4 + 32x^3 + 24x^2 + 8x + 1`

Explanation:

`(2x+1)^4 = frac{4!}{4!0!}(2x)^4(1)^0 + frac{4!}{3!1!}(2x)^3(1)^1 + frac{4!}{2!2!}(2x)^2(1)^2 + frac{4!}{1!3!}(2x)^1(1)^3 + frac{4!}{0!4!}(2x)^0(1)^4`

`= 1(2x)^4 + 4(2x)^3 + 6(2x)^2 + 4(2x)^1 + 1(2x)^0`

`= 16x^4 + 32x^3 + 24x^2 + 8x + 1`