Pre-Calculus Section 8.5a Binomial Expansion. Calculator Help Graphing calculator has n C r button. Math - PRB - nCr You must enter the n# before.

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Presentation transcript:

Pre-Calculus Section 8.5a Binomial Expansion

Calculator Help Graphing calculator has n C r button. Math - PRB - nCr You must enter the n# before

Remember? (x + y) 0 (x + y) 1 (x + y) 2 (x + y) 3

Binomial Theorem Expands a binomial to any power (x + y) n = x n + nx n-1 y + …. + n C r x n-r y r +….nxy n-1 + y n * there are n + 1 terms * the power of the first term = n * the power of the last term = n

* the power of the rest of the terms decreases by 1 from left to right * the power of the rest of the terms decreases by 1 from right to left * the exponents add to equal n * find the coefficients using n C r * if subtracting alternate the signs

Write the expansion of (x + 2) 3 Binomial Expansion Coefficients: n = exponent the first term has a power of 3 3 C 0 = 1 st coefficient 3 C 1 = 2 nd coefficient 3 C 2 = 3 rd coefficient 3 C 3 = 4 th coefficient

5.Write the expansion of (x + 2) 3

6.Write the expansion of (y - 7) 4

7.Write the expansion of (x + y) 5

8.Write the expansion of (3x + 2y) 6

Homework: Page – 10Evens 18 – 26Evens