What is the binomial expansion of #(x+2)^5#?

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Answer 1 · 2015-07-19T12:42:07

#(x+2)^5 = x^5+10x^4+40x^3+80x^2+80x+32#

Write out the #6#th row of Pascal's triangle as a sequence:

#1, 5, 10, 10, 5, 1#

Write out ascending powers of #2# from #2^0# up to #2^5# as a sequence:

#1, 2, 4, 8, 16, 32#

Multiply the two sequences together to get:

#1, 10, 40, 80, 80, 32#

These are the coefficients of the expansion:

#(x+2)^5 = x^5+10x^4+40x^3+80x^2+80x+32#