Question

How do you find the binomial expansion of `(x + 2y)^7`?

Answer 1

Use Pascal's triangle for the base coefficient terms

Explanation:

Pascal's Triangle
#{: ("exponent", "|","term", , , , , , , ), ( 0, "|", 1 , , , , , , , ), ( 1, "|", 1, 1, , , , , , ), ( 2, "|", 1, 2, 1, , , , , ), ( 3, "|", 1, 3, 3, 1, , , , ), ( 4, "|", 1, 4, 6, 4, 1, , , ), ( 5, "|", 1, 5,10,10, 5, 1, , ), ( 6, "|", 1, 6,15,20,15, 6, 1, ), ( 7, "|", 1, 7,21,35,35,21, 7, 1) :}#

`(x+2y)^7`
`=1x^7(2y)^0+7x^6(2y)^1+21x^5(2y)^2+35x^4(2y)^3+35x^3(2y)^4+21x^2(2y)^5+7x^1(2y)^6+1x^0(2y)^7`

(evaluation of individual terms is left as a basic exercise in arithmetic)