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2.3 Binomial ExpansionsBinomial ExpansionThis is the binomial expansion of (5y3-2)3Binomial Expansionn=0, (a+b)0=1n=1, (a+b)1=a+bn=2, (a+b)2=a2+2ab+b2n=3, (a+b)3=a3+3a2b+3ab2+b3n=4, (a+b)4=a4+4a3b+6a2b2+4ab3+b4n=5, (a+b)5=a5+5a4b+10a3b2+10a2b3+5ab4+b5 =a5b0+5a4b1+10a3b2+10a2b3+5a1b4+a0b5Pascal Triangle11a+1b1a2+2ab+1b21a3+3a2b+3ab2+1b31a4+4a3b+6a2b2+4ab3+1b41a5+5a4b+10a3b2+10a2b3+5ab4+1b5

n=0n=1n=2n=3n=4n=5TAKE NOTE!The signs of the terms alternate between + and when a or b is a negative number.Try it!Formula for coefficient from Pascal's Triangle

Binomial TheoremBinomial TheoremTry it!ExampleTry it!Specific Term of an ExpansionExample 2Example 3 Example 4Example 5Try it!Expansion of (1+x)n where n is a Rational NumberExample 1Example 2Example 3Try it!