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The binomial theorem tells us that the expansion of EQN:(x+y)^n is given by:

where the EQN:c_i are the binomial coefficients.

Writing the expansion using the binomial coefficients we get:

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${n\choose~0}x^n+{n\choose~1}x^{n-1}y+{n\choose~2}x^{n-2}y^2+{n\choose~3}x^{n-3}y^3+\ldots+{n\choose~n}y^n$

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The coefficients are exactly the numbers in the appropriate row of Pascal's Triangle.