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

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Answer 1 · 2015-07-09T21:59:37

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

Pascal's triangle is

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#