Whose?

Algebra Level 2

( x + y ) n = x n + n x n 1 y + n ( n 1 ) 1 2 x n 2 y 2 + n ( n 1 ) ( n 2 ) 1 2 3 x n 3 y 3 + + n ( n 1 ) ( n 2 ) 1 2 3 x 3 y n 3 + n ( n 1 ) 1 2 x 2 y n 2 + n x y n 1 + y n \large{(x+y)^n=x^n+nx^{n-1}y+\frac{n(n-1)}{1*2}x^{n-2}y^2+\frac{n(n-1)(n-2)}{1*2*3}x^{n-3}y^3+\cdots} \\ \large{+\frac{n(n-1)(n-2)}{1*2*3}x^{3}y^{n-3}+\frac{n(n-1)}{1*2}x^{2}y^{n-2}+nxy^{n-1}+y^n}

Name this theorem!

Exponential theorem Euler's theorem Bloons Qoth's Theorem Binomial theorem Leibniz theorem

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2 solutions

Hung Woei Neoh
Jul 9, 2016

The theorem for the expansion of ( x + y ) n (x+y)^n is known as the binomial theorem

Though I'm very curious, what is the Bloons Qoth's Theorem?

I googled it and it came up with pictures of quotes! It's a fake!

Rico Lee - 4 years, 11 months ago

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Well, the person who posted this is @Bloons Qoth ...

Hung Woei Neoh - 4 years, 11 months ago

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Yup.... Bloons Qoth what's your theorem?

A Former Brilliant Member - 4 years, 11 months ago

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@A Former Brilliant Member 9+10=21

It's also a joke by the way

Bloons Qoth - 4 years, 11 months ago

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@Bloons Qoth Lemme guess... I X + X IX+X ?

Hung Woei Neoh - 4 years, 11 months ago

This is the Binomial Theorem .

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