Question

How do you use the binomial `(x+2y)^5` using Pascal's triangle?

Answer 1

`= color(blue)(x^5 + 10x^4y + 40 x^3 y^2 + 80 x^2 y^3 + 80 xy^4 + 32y^5`

Explanation:

1 5 10 10 5 1 pattern

`a = x, b = 2y`

`(x + 2y)^5 = 1 * x^5 (2y)^0 + 5 x^4 (2y) + 10 x^3 (2y)^2 + 10 x^2 (2y)^3 + 5 x (2y)^4 + 1 x^0 (2y)^5`

`= color(blue)(x^5 + 10x^4y + 40 x^3 y^2 + 80 x^2 y^3 + 80 xy^4 + 32y^5`