Finding the Coefficient of x^2*y^3*z in a Polynomial Expansion

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To find the coefficient of x^2*y^3*z in the polynomial (2x - y^2 + 3z)^6, the binomial theorem can be applied. The discussion suggests that while one could expand the polynomial fully, a more efficient method involves using combinations and the multinomial expansion. The coefficients from the terms 2, -1, and 3 must be considered in calculating the final coefficient. Clarification is sought on whether the intended term was x^2*y^3*z or x^2*y^6*z, indicating potential confusion in the original question. The conversation emphasizes the importance of understanding polynomial expansions for accurate coefficient determination.
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What is the coeffcient of x^2*y^3*z in the polynomial(2x-y^2+3z)^6?
please give me an example, and how do i deal with coeffienct that is inside the function 2, -1, and 3.
 
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You could always do it the long way...and multiply it all out and see what the coefficient is...but I imagine you're asking is there an easier way right?
 
The coefficient x^2*y^3*z is really easy. Are you sure you didn't mean x^2*y^6*z ?
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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