How do I use Pascal's triangle to expand #(x + 2)^5#?

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Answer 1 · 2015-07-09T22:18:59

You write out the sixth row of Pascal's triangle and make the appropriate substitutions.

Pascal's triangle is

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The numbers in the fifth row are 1, 5, 10, 10, 5, 1.

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

#(x+y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5#

But our polynomial is #(x+2)^5#.

#(x+2)^5 = x^5 + 5x^4×2 + 10x^3×2^2 + 10x^2×2^3 + 5x×2^4 + 2^5#

#(x+2)^5 = x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32#