Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Expand a binomial with coefficients inside the terms using Pascal's Triangle
Problem
Expand \((2x~+~3)^3\).
Big Picture
What this problem is really about
Treat each binomial entry as one complete object before applying the cube pattern. The outside exponents act on internal numerical coefficients as well as variables, so substitute the unsimplified compound terms into all four slots first. Then simplify each slot separately and check that the variable degree decreases one step at a time.
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