MHB Order of operations doubt on this expression

AI Thread Summary
The expression $\frac{1}{2}*2x*x-2$ can be evaluated in two ways, leading to different results. The first method simplifies directly to $x^2 - 2$, while the second method incorrectly applies the order of operations, resulting in $x^2 - 1$. The discrepancy arises from the interpretation of the expression; the order of operations dictates that multiplication should be prioritized over subtraction. The correct interpretation confirms that the first method is valid. Understanding the proper application of the order of operations is crucial for consistent results.
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Let's say that we have this expression,

$\frac{1}{2}*2x*x-2$

So now solving this in one method we can

$\frac{1}{\cancel 2}*\cancel2x*x-2=x^2-2$

In another way

$\frac{1}{2}*2x*x-2=\frac{2x^2-2}{2}=x^2-1$

What is the reason that I get two different answers ? I hope that both ways are valid

Many THanks :)
 
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The order of operations dictates that we do multiplication/division first before subtraction, so the first method is correct. The second method you used would be valid if we had:

$$\frac{1}{2}(2x\cdot x-2)$$
 
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