math m coursework.doc4

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RESULT When a binomial expression such as ( a +b) is raised to the power of n where n is a small positive integer, a binomial expansion of the form ( a+ b) n is obtained such as follows:- When n=0, ( a +b) 0 =1 n=1, ( a +b) 1 =a+b n=2, ( a +b) 2 =( a +b)( a+b ) ¿ a 2 +ab+ab+ b 2 ¿ a 2 +2 ab +b 2 n=3, ( a +b) 3 =( a +b) ¿ ¿ ( a +b) ( a 2 +2 ab+b 2 ) ¿ a 3 + 2 a 2 b +ab 2 +a 2 b+ 2 ab 2 + b 3

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Math M Course work

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Page 1: Math M Coursework.doc4

RESULTWhen a binomial expression such as (a+b ) is raised to the power of n where n is a small positive integer, a binomial expansion of the form (a+b)n is obtained such as follows:-

When n=0, (a+b )0=1

n=1, (a+b )1=a+b

n=2, (a+b )2=(a+b ) (a+b )

¿a2+ab+ab+b2

¿a2+2ab+b2

n=3, (a+b )3= (a+b )¿

¿ (a+b )(a2+2ab+b2)

¿a3+2a2b+ab2+a2b+2ab2+b3