Question

How do you expand `(2a+b)^6`?

Answer 1

`color(blue)(64 a^6 + 192 a^5 b + 240 a^4 b^2 + 160 a^3 b^3 + 60 a^2 b^4 + 12 a b^5 + b^6)`

Explanation:

1 6 15 20 15 6 1

Using Pascal's triangle,
(x+y)^6 where
x = 2a & y = b

`(2a+b)^6 = 1 * (2a)^6 + 6 (2a)^5 b + 15 (2a)^4 b^2 + 20 (2a)^3 b^3 + 15 (2a)^2 b^4 + 6 (2a) b^5 +1 * b^6`

`64 a^6 + 192 a^5 b + 240 a^4 b^2 + 160 a^3 b^3 + 60 a^2 b^4 + 12 a b^5 + b^6`