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

1 Answer
Jul 19, 2015

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#

Explanation:

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#