Expansion & Factoring Tool
Special products, the binomial theorem to any power with Pascal's triangle drawn live, and the aⁿ − bⁿ family of factorizations. Covers §2.7–2.8 of the algebra material.
Binomial Expansion (a + b)ⁿ
Pascal's triangle down to row n — your coefficients highlighted. FIG. T11-1
aⁿ − bⁿ and aⁿ + bⁿ Factorizations
a − b divides aⁿ − bⁿ for every n; a + b divides aⁿ + bⁿ only when n is odd (and aⁿ − bⁿ when n is even, via the difference of the even powers). These identities are the backbone of factoring beyond quadratics.