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Calculus/multiplying polynomials

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Expert: Scotto - 8/27/2008


Question
2x(-3x+3)(-2x+6)  

when i multiply by 2x first i get
24x^4-96x^3+72x^2

when i multiply the parentheses together first i get
12x^3-48x^2+36x  

how is this happening?  is there a specific rule for when to multiply what?  i was under the impression that it doesn't matter what order you do multiplication in.

Answer
There are two ways to multiply this problem.
(2x(-3x+3))(-2x+6) or 2x((-3x+3)(-2x+6)).
The first way you did the problem involved multiply both the first and second set of parenthises by 2x.  This is only done if the parenthises are added together, as in ((-3x+3) + (-2x+6)), in which case we get an entirely different answer.

Consider 2*(3*5).  This is clearly 30.  In your first approach to the problem, this would be said to be 2*3 * 2*5 = 6*10 = 60.  Looking at the real answer, we can see we multiplied by an extra 2.

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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