Bionomial Theorem

a) write down the expansion of (3x+5)3 and deduce the expansion for (3x-5)3 b) Hence find the exact solutions to the equation (3x+5)3 - /93x-5)3 = 730

Answers
According to the binomial theorem (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 So (3x+5)^3 = 27x^3 + 135x^2 + 225x + 125 and (3x-5)^3 = 27x^3 - 135x^2 + 225x - 125
javaid.aslam
07 February 2011
According to the binomial theorem, (a+b)^3 = a^3 + 3a^2b + 3ab^2 +b^3 (a) In your question, a=3x and b=5, so (3x+5)^3 = (3x)^3 + (3((3x)^3)5) + (3(3x)(5^2)) + (5^3) = 27x^3 +135X^2 + 225X +125 Using the above, we can deduce the solution for (3x-5)^3 as follows: (3x-5)^3 = (3x)^3 + (3((3x)^3)(-5)) + (3(3x)((-5)^2)) + ((-5)^3) = 27x^3 -135X^2 + 225X -125 (b) Using the results from part(a), we get that ((3x+5)^3) -((3x-5)^3) = 270x^2 + 250 = 730 270x^2 = 730 - 250 x^2 = (480/270) = (16/9) Therefore, x = +/- sqrt(16/9) = +/- (4/3) Hence, the exact solutions to the equation are +(4/3) and -(4/3). Hope this helps.
msftutor
07 February 2011
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