Find the sum of all coefficients in expansion of $(x^2+2x)^{20}$.
Is there a specific method or formula for this?
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7Yes, there is. Do you know another way to describe the sum of the coefficients of a polynomial $P(x)$? – Daniel Fischer Aug 12 '14 at 13:01
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6Nice hint, @Daniel! Let's hope no one spoils it. Satvik - you can figure it out! – Jyrki Lahtonen Aug 12 '14 at 13:03
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2f(1) is the sum.. – next Aug 12 '14 at 13:03
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1Compare the form of the binomial expansion with the sum of the coefficients. Is there an $x$ for which they agree? (You could also try with a smaller exponent and look for a pattern.) – Semiclassical Aug 12 '14 at 13:04
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The sum of the coefficients of a polynomial is just the value that such polynomial takes in $1$, hence: $$\sum_{n\geq 0}[x^n](x^2+2x)^{20} = (1+2)^{20} = 3^{20}.$$
Jack D'Aurizio
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