Matrix Chain teaches the core interval DP pattern: for a range, try all split points, iterate by length. The formula has three parts: cost of left range dp[i][k], cost of right range dp[k+][j], and cost of combining them.
This exact structure appears in many problems. The "combining cost" changes, but the framework stays the same. Parenthesization, optimal BST, and burst balloons all share this -part structure.