Extremely confused about this Basic algebra
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Extremely confused about this Basic algebra
What is wrong with taking a half out as a factor and going
I know it's wrong, but I can't see exactly what is wrong with it, I would appreciate a detailed answer and not something like
thnxLast edited by member910132; 21-05-2012 at 11:55. -
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Re: Extremely confused about this Basic algebraYou can't really get a better explanation than the one you wouldn't like to be given.(Original post by member910132)
What is wrong with taking a half out as a factor and going
I know it's wrong, but I can't see exactly what is wrong with it, I would appreciate a detailed answer and not something like
thnx
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Re: Extremely confused about this Basic algebraWell, you could prove it to yourselve geometrically if you let a and b be the sides of a rectangle. Calculate its area (ab), and then shink each length by a half and calculate the new area (0.5a*0.5b) - you'll find that the new area is percisely one quarter of the original area, and not one half of the original area.
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Re: Extremely confused about this Basic algebraThnx, PRSOM !(Original post by oo00oo)
Well, you could prove it to yourselve geometrically if you let a and b be the sides of a rectangle. Calculate its area (ab), and then shink each length by a half and calculate the new area (0.5a*0.5b) - you'll find that the new area is percisely one quarter of the original area, and not one half of the original area. -
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Re: Extremely confused about this Basic algebraYou are just getting confused with sums and products, that is all.
(i)
but
(ii)
.
With
a whole number, you demonstrate (i) by rearranging the left had side to give
where there are the same number of sums on each side.
On the other hand (ii) would look like
![\lambda a \times \lambda b = (a+\cdots+a) \times (b+\cdots + b) = \begin{array}[c] \mbox{}a(b+ \cdots + b) \\ + \\ \vdots \\ + \\ a(b+\cdots + b) \end{array}](http://www.thestudentroom.co.uk/latexrender/pictures/e5/e59468ab32fe4c6913716e68db7085e2.png "\lambda a \times \lambda b = (a+\cdots+a) \times (b+\cdots + b) = \begin{array}[c] \mbox{}a(b+ \cdots + b) \\ + \\ \vdots \\ + \\ a(b+\cdots + b) \end{array}")
![= \begin{array}[c] \mbox{}ab + \cdots + ab \\ + \\ \vdots \\ + \\ ab+\cdots + ab \end{array}](http://www.thestudentroom.co.uk/latexrender/pictures/ac/acc4aaa1ba68c6d6584801215a38e22d.png "= \begin{array}[c] \mbox{}ab + \cdots + ab \\ + \\ \vdots \\ + \\ ab+\cdots + ab \end{array}")
i.e. when you expand out the brackets you can think of a
square array of the terms 
.
