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Binomial Theorm

mustish1
mustish1 asked
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a. What is Binomial theorem ?
b. How to use the binomial theorem to expand (3x-5) Power 4

Thanks.
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ozo
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Commented:
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Commented:
Hi

THE BINOMIAL THEOREM shows how to calculate a power of a binomial -- (a + b)n -- without actually multiplying out.

For example, if we actually multiplied out the 4th power of (a + b) --

(a + b)4 = (a + b)(a + b)(a + b)(a + b)

-- then on collecting like terms, we would find

(a + b)4 = a4 + 4a3b + 6a²b² + 4ab3 + b4


Now there is a trick of calculating coefficients

see the following link how calculate coefficient\

http://www.regentsprep.org/Regents/math/algtrig/ATP4/bintheorem.htm


There are some other useful links about it
http://www.mathsisfun.com/algebra/binomial-theorem.html
http://www.purplemath.com/modules/binomial.htm
http://en.wikipedia.org/wiki/Binomial_theorem 
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Commented:
and your b question is a real mess to type out. It would take me about 1/2 hour of typing.
the usual binomial is a relation of the form (x + y)^n where in your case x = 3x and y = 5 and n = 4.
The answer is
x^4 + x^3(y) + x^2(y^2) + x^1(v^3) + y^4 with a coefficient in front of each term.
The (r + 1)coefficient is given by the number of combinations of n things taken r at a time.
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Commented:
that is, your y is -5     I left out the - sign above
deightonprog
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Commented:

(a + b) ^ 4= a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

putting
a = 3x
b = -5


(3x-5)^4 = (3x)^4 + 4(3x)^3(-5) + 6(3x)^2(-5)^2 + 4(3x)(-5)^3 + (-5)^4

= 81x^4 - 540x^3 + 1350x^2 - 1500x + 625

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