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Person's question at Yahoo! Answers regarding the application of the binomial theorem

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MarkFL

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Feb 24, 2012
13,775
Here is the question:

How to expand this binomial expansion?


a.) (x - 2y)^3

with the equation:

(n over r) x [a^(n-r)] x (b^r)

Thank you!!!
I have posted a link there to this topic so the OP can see my work.
 
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MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Hello Person,

The binomial theorem may be stated as:

\(\displaystyle (a+b)^b=\sum_{r=0}^{n}{n \choose r}a^{n-r}b^r\)

And so, for the given binomial to be expanded, we have:

\(\displaystyle (x-2y)^3=(x+(-2y))^3=\sum_{r=0}^{3}{3 \choose r}x^{n-r}(-2y)^r\)

\(\displaystyle (x-2y)^3={3 \choose 0}x^3(-2y)^0+{3 \choose 1}x^2(-2y)^1+{3 \choose 2}x^1(-2y)^2+{3 \choose 3}x^0(-2y)^3\)

\(\displaystyle (x-2y)^3=1\cdot x^3\cdot1+3x^2(-2y)+3x(-2y)^2+1\cdot1\cdot(-2y)^3\)

\(\displaystyle (x-2y)^3=x^3-6x^2y+12xy^2-8y^3\)