Educator

Binomial Theorem

• The expansion of (a + b)ⁿ has n + 1 terms.

• In the kth term of (a + b)ⁿ , the exponent of b is k – 1 and the exponent of is n – (k – 1).

• In the kth term, the coefficient has k – 1 factors in the numerator and the denominator.

• You can always find the coefficients of the expansion or of a particular term by writing out Pascal’s triangle and using row n.

• The coefficients of the expansion are symmetrical around the middle term. So once you have found the first half of the coefficients, you already have the coefficients for the rest of the terms. They are the same ones you have found but listed in reverse order.