Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Expand a binomial using Pascal's Triangle and the power pattern
Problem
Expand \((x~-~y)^4\).
Big Picture
What this problem is really about
Build the expansion in three layers: coefficient magnitudes from Pascal’s row, complementary powers of the two variables, and signs from the negative second term. Treat subtraction as addition of a negative quantity. Even powers of that negative term are positive and odd powers are negative, so the signs alternate without changing the exponent pattern.
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