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2. Simplify (2x^3 + 9x - 12) - (3x^3 -9)

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The expression is the following:


(2x^3+9x-12)-(3x^3-9)

First, we need to evaluate the parenthesis. The first one doesn't have any factors multiplying, dividing or another opration that require it, so we can just remove it:


2x^3+9x-12-(3x^3-9)

Now, the second parenthesis have a "-" sign in front of it, so we need to distribute this sign to each term inside the parenthesis. We can think of it as multiplying each term by "-1":


\begin{gathered} 2x^3+9x-12-(3x^3-9) \\ 2x^3+9x-12-3x^3+9 \end{gathered}

No, we pair the like term. Like terms can be classifyied by the x part and its exponent. We have 3 types here, the ones without x, the ones with x to the first (simply x) and the one with x to the third (x³).


2x^3-3x^3+9x-12+9

And now we evaluate the like terms to get the simplifyed expression:


-x^3+9x-3

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