MathRevolution wrote:
If x>0, y<0 and z<0,\((|x|+|y|+|z|)^2\)=?
A. \(x^2+y^2+z^2+2xy+2yz+2zx\)
B.\(x^2+y^2+z^2+2xy-2yz+2zx\)
C.\(x^2+y^2+z^2-2xy+2yz-2zx\)
D. \(x^2+y^2+z^2-2xy-2yz-2zx\)
E.\(x^2-y^2-z^2+2xy+2yz+2zx\)
* A solution will be posted in two days.
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Remember that these kind of question can be tricky if you don't apply the last trick after sorting your reasoning.
The reasoning is anything that comes out of mod is always positive . It can not be negative.
But the last part of the trick that many of us forget to apply is to check whether your answers depends on the absolute value (value that comes out of the mod) or on the "raw value" that is the original original value of the integer without the mod (values with original polarity -ve or +ve)
IN THIS QUESTION:- value of y and z are negative
SO the expression \((|x|+|y|+|z|)^2\) will always be positive
You don't have to worry about terms with square. because squaring kills negative polarity so x^2, y^2 and z^2 are not our worries.
Now to get a positive value from the options that contains "Raw values" and not the "absolute values" you must remember that x is +ve and y and z are -ve , so if they are multiplied with x their product will be negative. You have to remove that negative polarity . What is the easiest way of removing a negative polarity ? multiply it with -1 or simply -
Therefore all terms that contains either y or z should be multiplied with -1 to give us terms that are positive,
so our answer should contains -2xy and -2xz
Also because -y and -z will multiply to give +yz we don't have to multiply it with -1
finally our expression should look like
\(x^2+y^2+z^2 - 2xy +2yz-2xz\)
THAT IS OPTION C
C is the answer
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