5.7 The Binomial Theorem Name: ___________________ Objectives: Students will be able to expand a binomial using Pascal's Triangle. Students will be able to use the Binomial Theorem. There are numerical patterns in the expansion of powers of binomials. Let's examine the expansion of (x + y)n. (x + y)0 = (x + y)1 = (x + y)2 = (x + y)3 = (x + y)4 = (x + y)5 = 1x0y0 1x1y0 + 1x0y1 1x2y0 + 2x1y1 + 1x0y2 1x3y0 + 3x2y1 + 3x1y2 + 1x0y3 0 4 1x4y0 + 4x3y1 + 6x2y2 + 4x1y3 + 1x y 0 5 1 4 1x5y0 + 5x4y1 + 10x3y2 + 10x2y3 + 5x y + 1x y Dec 191:49 PM Let's look at the coefficients only. Dec 191:49 PM 1 If just the coefficients are extracted and arranged in a triangular array, they form a pattern called _______________. 1 1 1 1 2 1 A Bit of History Blaise Pascal (1623-1662) Blaise Pascal was a ___________________, __________, _________, _________ and ________________. He invented the _________________. His greatest influences have been in the fields of _________________ and _________________. Dec 191:50 PM The Binomial Theorem gives a general formula for expanding a binomial using Pascal's Triangle. We'll look at some examples below. Expand each binomial using the Binomial Theorem. 2.) (a + b)8 1.) (x + y)6 Dec 191:51 PM 2 4.) (4a + 3b)7 3.) (2x - y)6 Dec 191:54 PM 5.7 ICE Name: ________________ Expand each binomial using the Binomial Theorem. 1.) (x - 5)4 2.) (5a + 2b)3 Dec 191:54 PM 3 Jan 29:41 AM 4
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