# Coefficient of x^3

by Stacyg
Tags: coefficient
 P: 25 Find the coefficient of x^3 in the expansion of (2x^2-3/x)^3 I know how to do simple coefficients using pascalles triangle but I really don't know how to do this. Any help would be much appreciated.
 P: 738 Write it as $$(2x^2 - 3x^{-1})^3$$ From Pascal's triangle, you know how to expand $$(a+b)^n$$ What can you replace with a and what can you replace with b?
 HW Helper P: 6,202 $$(2x^2-\frac{3}{x})^3$$ $$(\frac{1}{x}(2x^3-3))^3$$ How about now?
 P: 738 Coefficient of x^3 Oh, that's a nice way of doing it :)
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P: 6,202
 Quote by Tedjn Oh, that's a nice way of doing it :)
Usually (well for me), a binomial expansion is usually done with a variable and a constant.

as for $(a+b)^n$ is valid for $|\frac{b}{a}|<1$ But if a and b are variables, you'll have to do some fancy algebra to get the range for which it is valid.
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Thanks
P: 25,235
 Quote by rock.freak667 Usually (well for me), a binomial expansion is usually done with a variable and a constant. as for $(a+b)^n$ is valid for $|\frac{b}{a}|<1$ But if a and b are variables, you'll have to do some fancy algebra to get the range for which it is valid.
Why is it only valid in some range??? I also don't see why you need to factor the original. (a+b)^3=a^3+3*a^2*b+3*a*b^2+b^3. Just put a=2x^2 and b=(-3/x), figure out which term is the x^3 term and evaluate it.
 HW Helper P: 6,202 That's what I was taught.."validity of a binomial"
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Thanks
P: 25,235
 Quote by rock.freak667 That's what I was taught.."validity of a binomial"
Got a reference? If you are thinking of the convergence of the infinite series for negative exponents, that is something to think about. But this is a positive exponent, the series is finite. There are no convergence issues.
 P: 63 Besides, we're dealing with polynomials in the case of (a+b)^n