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

1 Answer
Jan 28, 2018

Answer:

#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:

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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#