How do you use the binomial series to expand #(x - y)^6#?

1 Answer
Oct 16, 2016

Answer:

#color(green)(x^6-6x^5y+15x^4y^2-20x^3y^3+15x^2y^4-6xy^5+y^6#

Explanation:

#color(blue)((x-y)^6#

Let's use the pascal's triangle to solve it

enter image source here

So,

#underbracecolor(blue)((x-y)^6)#

#underbrace(color(indigo)(1)color(blue)((x^6)(-y^0))+color(indigo)(6)color(blue)((x^5)(-y^1))+color(indigo)(15)color(blue)((x^4)(-y^2))+color(indigo)(20)color(blue)((x^3)(-y^3))+color(indigo)(15)color(blue)((x^2)(-y^4))+color(indigo)(6)color(blue)((x^1)(-y^5))+color(indigo)(1)color(blue)((x^0)(-y^6))#

#underbrace(color(indigo)(1)color(blue)((x^6))-color(indigo)(6)color(blue)((x^5)(y))+color(indigo)(15)color(blue)((x^4)(y^2))-color(indigo)(20)color(blue)((x^3)(y^3))+color(indigo)(15)color(blue)((x^2)(y^4))-color(indigo)(6)color(blue)((x)(y^5))+color(indigo)(1)color(blue)((y^6))#

#color(green)(x^6-6x^5y+15x^4y^2-20x^3y^3+15x^2y^4-6xy^5+y^6#

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