Question

Expand the following using either the Binomial Theorem or Pascal’s Triangle. You must show your work for credit.. . (2x + 4)^3

Answer 1

A Pascal triangle is the triangular way of expanding a binomial. So the best way in expanding that function is thru Binomial Theorem and the expanded for of it is 8x^3+48x^2+98x+64

Answer 2

Before even trying to put this into the binomial form, we must figure out the coefficients. If we go by the Pascal's Triangles way we should end up with:

        1

    1      1

 1     2     1

1    3     3    1

Going by the last level (which is the third level) we get 3C0:1, 3C1:3, 3C2:3, 3C3:1.

Now with the equation: (a+b)^3 = 3C0a^3 + 3C1a^2 b + 3C2a b^2 + 3C3b^3 we just plug in all the values and simplify

(2x+4)^3 = 2x^3 + 3(2x)^2 (4) + 3(2x) (4)^2 + (4)^3

(2x+4)^3 = 8x^3 + (3)(4x^2)(4) + (3)(2x)(16) + 64

Then we finally end with: (2x+4)^3 = 8x^3 48x^2 + 96x +64