How do you expand # (2x + y)^4 # using Pascal’s Triangle?

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Answer 1 · 2015-07-19T12:50:14

Combine the #5#th row of Pascal's triangle and a sequence of powers of #2# to find the coefficients of the expansion:

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

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

#1, 4, 6, 4, 1#

Write out descending powers of #2# from #2^4# to #2^0# as a sequence:

#16, 8, 4, 2, 1#

Multiply the two sequences together to get:

#16, 32, 24, 8, 1#

These are the coefficients of the expansion:

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