What is the Binomial Expansion of #(2+x)^4#?

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Answer 1 · 2015-06-29T20:30:19

#(2+x)^4 = 16+32x+24x^2+8x^3+x^4#

Write out the 5th row of Pascal's triangle as a sequence:

#1, 4, 6, 4, 1#

Write out the powers of #2# from #2^4# down to #2^0#:

#16, 8, 4, 2, 1#

Multiply the two sequences together to get:

#16, 32, 24, 8, 1#

These are the coefficients of the binomial expansion:

#(2+x)^4 = 16+32x+24x^2+8x^3+x^4#