How do you use pascals triangle to expand #(2s+1)^4#?

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Answer 1 · 2015-07-17T21:12:30

Combine the 5th row of Pascal's triangle with descending powers of #2# to find:

#(2s+1)^4 = 16s^4+32s^3+24s^2+8s+1#

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

#1#, #4#, #6#, #4#, #1#

Write out powers of #2# in descending order from #2^4# to #2^0#:

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

Multiply these two sequences together to get:

#16#, #32#, #24#, #8#, #1#

These are the coefficients of the powers of #s# in the expansion:

#(2s+1)^4 = 16s^4+32s^3+24s^2+8s+1#