Add or subtract, as indicated.

Question

- (8 x^{3} + x - 3) + (2 x^{3} + x^{2}) - (4 x^{2} + 3 x - 1)

Accepted Answer

Hello. Today we're going to be performing the given addition and subtraction. So what we are given is negative four M cubed plus two M minus five plus the quantity five M cubed plus three M squared minus seven M squared plus five M minus four. So in order to add these quantities together we're going to first need to open up the parentheses in order to do that. We're going to have to distribute negative one into the first quantity for M cubed plus two M minus five. Next we're going to distribute positive one into the quantity five M cubed plus three M squared. But that's not gonna change this quantity at all. So we can go ahead and just remove the parentheses and finally we're going to distribute negative one into seven M squared plus five M minus four. And that's gonna open up that set of parentheses. So negative one times four M cubed is going to give us negative four M cubed negative one times two. M is going to give us negative two M and negative one times negative five is going to give us positive five. Next we're going to distribute one into five Mq plus three M squared. But that doesn't change anything. So what we are left with is positive five M cubed plus three M squared. And finally we're going to distribute negative one into the last quantity. So negative one times seven M squared is going to give us negative seven M squared negative one times five M is going to give us negative five M. And finally negative one times negative four is going to give us positive four. So what we have here is the original quantity but with the parentheses removed in order to simplify this, we're going to need to combine the like terms together. So what we can go ahead and do is combine the m cubed terms together, which is going to be negative four M cubed and positive five M cubed. Next we're going to combine the m square terms together which is going to be positive three M squared and negative seven M squared. Next we're gonna combine the M terms together which is negative two M and negative five M. And finally we're going to go ahead and combine our constants which is going to be positive five and positive four. So if we combine the like terms together, negative four M cubed plus five M cubed is going to give us positive M cubed. Next we're going to write the m square terms and positive three M squared minus seven M squared is going to give us negative four M squared. Next we're going to write the M terms and negative to m minus five M is going to give us negative seven M. And finally five plus four is going to give us positive nine. And this is going to be the simplified some of the original quantities and with that being said, the answer to this problem is going to be C. So I hope this video helps you in understanding how to take this some, and I'll go ahead and see you all in the next video.

Add or subtract, as indicated. $- (8 x^{3} + x - 3) + (2 x^{3} + x^{2}) - (4 x^{2} + 3 x - 1)$

Key Concepts

Polynomial Addition and Subtraction

Like Terms

Distributive Property

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