Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer United States

Problem:
What is the sum of the coefficients of the expansion (x+2y1)6(x+2y-1)^6?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
The sum of the coefficients of a polynomial is that polynomial evaluated at 11, which for the question at hand is (1+211)6=26=64(1+2 \cdot 1-1)^6 = 2^6 = 64.

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