MHB Apply Binomial Theorem: Expand (x-2y)^3

[MarkFL]

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.

 

[MarkFL]

Hello Person,

The binomial theorem may be stated as:

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

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

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

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

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

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