What is meant by a power of a binomial?

1 Answer
Aug 29, 2015

Answer:

The power of a binomial is the value of #n# in the binomial expression #(a+x)^n#.

Explanation:

For any value of #n#, the #n^"th"# power of a binomial is given by:

#(x+y)^n=x^n +nx^(n-1)y +(n(n-1))/2x^(n-2)y^2 + … + y^n#

The general formula for the expansion is:

#(x+y)^n = sum_(k=0)^n (n!)/((n-k)!k!)x^(n-k)y^k#

The coefficients for varying #x# and #y# can be arranged to form Pascal's triangle.

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The #n^"th"# row in the triangle gives the coefficients of the terms in the #(n-1)^"th"# power of the polynomial.