georgiamadyson georgiamadyson
  • 27-01-2018
  • Mathematics
contestada

What is the coefficient of X^2 in the expansion of (X +2)^3

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nhienann nhienann
  • 27-01-2018
the coefficient is 2 !! I guess, I learned this a lot of years ago, sorry  
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altavistard
altavistard altavistard
  • 27-01-2018
     With simple elements such as x and 2, it's worth learning special products:

(a+b)^3 = a^3 + 3a^2b + 3a^b^2 + b^3

Thus, 

(x+2)^3 = x^3 + 3*2x^2) + 3(x)(2)^2 + 2^3

which simplifies to   x^3 + 6x^2 + 12x + 8.  The coeff. of x^2 is 6.

You could also use Pascal's Triangle to help you figure the coefficients.

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