How do you expand #(4x+y)^4# using Pascal’s Triangle?

Question

5064 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-04T18:48:28

Use a combination of a row of Pascal's triangle and a list of descending powers of #4# to find:

#(4x+y)^4 = 256x^4+256x^3y+96x^2y^2+16xy^3+y^4#

Write down the 5th row for Pascal's triangle as a sequence:

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

Write down the powers of #4# from #4^4# down to #4^0# as a sequence:

#256#, #64#, #16#, #4#, #1#

Multiply the two sequences together to get:

#256#, #256#, #96#, #16#, #1#

These are the coefficients of the expanded polynomial:

#(4x+y)^4 = 256x^4+256x^3y+96x^2y^2+16xy^3+y^4#