Question 328450
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (6x^2\ -\ 5)\ -\ (3x^2\ +\ x\ +\ 7)]


The first thing to do is to remove parentheses. The first set of parentheses has no lead coefficient, so you can just remove them without doing anything else.



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 5\ -\ (3x^2\ +\ x\ +\ 7)]


Notice that the second set of parentheses has a minus sign in front of it.  That is the same as saying there is a coefficient of -1 in front of that set of parentheses, thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 5\ +\ (-1)(3x^2\ +\ x\ +\ 7)]


Use the distributive property to remove this set of parentheses.  Effectively, you simply take off the parentheses and change every sign that was formerly inside of the parentheses -- including the understood + sign in front of the first term:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 5\ -\ 3x^2\ -\ x\ -\ 7]


Now you can combine like terms.  Terms with the same variable(s) AND the same exponent(s) are alike.  It is like adding up things on your kitchen table.  If you have 6 apples and 3 apples you can say you have 9 apples.  But if you have 6 apples and 3 cookies, that's all you can say:  6 apples and 3 cookies.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 3x^2\ =\ 3x^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5\ -\ 7\ =\ -12]


And there is no other term like *[tex \Large -x], so putting it all together:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x^2\ -\ x\ -\ 12]


And that is as simple as this one gets.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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