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(a+b)^n      Formula

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royalssaket123 | Student, Grade 9 | eNotes Newbie

Posted May 4, 2012 at 12:28 PM via web

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(a+b)^n

 

 

 

Formula

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rcmath | High School Teacher | (Level 1) Associate Educator

Posted May 4, 2012 at 7:50 PM (Answer #1)

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The binomial expansion formula states 

`(a+b)^n=sum_(k=0)^n(nCk)a^(n-k)b^k`

where the combination `nCk=(n!)/(k!(n-k)!)`

An example

`(x+4)^3=3C0x^3*4^0+3C1x^2*4^1+3C2x^1*4^2+3C3x^0*4^3`

`=x^3+3x^2*4+3x*16+4^3=x^3+12x^2+48x+64`

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