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

$c_0x^n+c_1x^{n-1}y+c_2x^{n-2}y^2+...+c_ny^n$

where the $c_i$ are the binomial coefficients. Writing the expansion using the binomial coefficients we get:

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

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

PascalsTriangle	(none)			(none)
↓	↓		↓	↓
BinomialCoefficient			(none)
			↓
		⇌	You are here BinomialTheorem
			↓
			PascalsTriangle
↓	↓		↓	↓
(none)	(none)			Factorial

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Binomial Theorem