How do I use Pascal's triangle to expand #(2x + y)^4#?

1 Answer
Jul 9, 2015

Answer:

Write out the fifth row of Pascal's triangle and make the appropriate substitutions.

Explanation:

Pascal's triangle is

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The numbers in the fifth row are 1, 4, 6, 4, 1.

They are the coefficients of the terms in a fourth order polynomial.

#(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4#

But our polynomial is #(2x+y)^4#.

#(2x+y)^4 = (2x)^4 + 4(2x)^3y + 6(2x)^2y^2 + 4(2x)y^3 + y^4#

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