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Unformatted text preview: 6:27 AM Thu Mar 7 -97% Alg2TrigH_-_Notes_9.5_-_2018.pdf D IS cont'd Binomial Expansion 2 of4 Note : There are several observations that should be made about the pattern and examples just listed . @ In each expansion, there are 'nt !"terms. 2 'x 'and y " have symmetrical roles. The powers of 'x'decrease by 1. by 1 in successive terms, whereas the powers of y "increase The sum of the powers of each term is "n't For instance 3+124 2+2-4 (xty)"= x'+ 4x'y tory 's try ty ? The coefficients of each term increase then decrease in symmetric pattern. This pattern is often called Pascal's Triangle. it proceeds at follows : (xty). = 1 7 0 throw (xty)'- Xty -> /st row (xty)* =x'+2xy +y" -> 2ad row ->1 21 37 row -1 3 3 1 eh+, hxE + K XE +(X = =(h4x) (xry)* =x'tyxy + bxay*+ /xy ' ty? -7 41 row ->1 4 6 4 1 This pattern can be continued forever. Note in the above triangle of numbers how each individual number is able to be created by adding the two numbers above it (with every row beginning and ending with U. The next two rows of the- triangle are shen Each row of the triangle alto corresponds to an nC, "volue . For example , taking the 6throw at shown abore : 20 you can verify these by hand or in the calculator. 50 to [MATH ] then +-- PROP and telect nCr . Fill in the numbers at needed. Scanned by CamScanner...
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