Mathematica(@mathemetica):From lines to cubes and beyond, the powers of (a + b) expand as (a + b)¹ = a + b, (a + b)² = a² + 2ab + b², (a + b)³ = a³ + 3a²b + 3ab² + b³, and (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴, with each term built from red a-blocks and blue b-blocks in matching quantities. Financial analysts expand (1 + r)ⁿ this way to project investment growth over n years under compound interest.

Mathematica

@mathemetica

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Mathematica@mathemetica

2026.07.25 04:56

From lines to cubes and beyond, the powers of (a + b) expand as (a + b)¹ = a + b, (a + b)² = a² + 2ab + b², (a + b)³ = a³ + 3a²b + 3ab² + b³, and (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴, with each term built from red a-blocks and blue b-blocks in matching quantities. Financial analysts expand (1 + r)ⁿ this way to project investment growth over n years under compound interest.