4-2 The Binomial Theorem Use Pascal’s Triangle to expand powers of binomials Use the Binomial Theorem to expand powers of binomials.

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Presentation transcript:

4-2 The Binomial Theorem Use Pascal’s Triangle to expand powers of binomials Use the Binomial Theorem to expand powers of binomials.

The pattern found in Pascal's triangle (shown below) can be used to determine the coefficients of an expanded binomial (a + b)n.

Expanding the binomial (a + b)n for nonnegative values of n requires finding the coefficient and the exponents for a and b in each term. Binomial expansions, such as in (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4, contain many patterns. The sum of the exponents in each term is n. In successive terms, the exponent of a decreases and the exponent of b increases. The coefficients are the entries in Pascal's triangle. There are n + 1 terms. The coefficients are symmetric

Expand the binomial.

Expand the binomial.

Expand the binomial. 18. 3𝑎−4𝑏 5 New 4-2 p239/ 1 – 6 all, 15, 18