Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) ...

Question

Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) - (2m³ + 5m² + 4m) + (m² - m)

Accepted Answer

Hello, everyone. For the following polynomial expression, we will perform the indicated operations to simplify. We are given the parentheses 18 K raised to the fourth power plus nine K squared plus two K minus the parentheses. Five K cubed minus five K squared plus six K plus the parentheses. Two K squared minus K. Our answer choices are a 18 K raised the fourth power minus five K cubed plus 16 K squared minus five K B 18 K raised the fourth power plus five K cubed plus six K squared plus seven K C 18 K raised the fourth power plus five K cubed plus two K squared plus nine K D 18 K raised to the fourth power minus five K cubed plus 12 K squared minus three K. I'm gonna begin by rewriting the expression. So we have the parentheses and then 18 K raised to the fourth power plus nine K squared plus two K closed parentheses minus the parentheses. Five K cubed minus five K squared plus six K, close parentheses plus the parentheses, two K squared minus K. So looking at the signs between my parentheses, I notice I have a minus sign between my 1st and 2nd set of parentheses. This means I need to distribute the negative into the parentheses as if I was multiplying in a negative one. And once I distribute that to each term in that parentheses, I can drop all of the parentheses for the entire expression. So I'm gonna start by rewriting the information that was in the first set of parentheses. 18 K raised the fourth power plus nine K squared plus two K and now distributing a negative into the parentheses that follows it. I have negative one multiplied by five K cubed. So that would be minus five K cubed. A negative multiplied by negative five K squared will give me a plus five K squared and a negative multiplied by six K will give us minus six K. And then my next sign is a plus. So I don't have to change anything in the third set of parentheses. I can just rewrite it as two K squared minus K. OK. So now we have a lot of terms, but I'm gonna start with the highest exponent and combine all my like terms along the way. I'm gonna cross them out once I use them. So I know I've used them the highest exponent I see here is a four. So our first term will be 18 K raise to the fourth power. There's nothing to combine it with. So it will be by itself. Next, I'm looking for any exponent of a three and it looks like I only have one term that has an exponent of three and that's negative five K cubed. So I write that into my answer and I'll continue on next, I'm looking for the exponent of two. So K squared, I have a positive nine K squared, a positive five K squared and a positive two K squared, adding all of those together, I will get a positive. So plus 16 K squared and now that they're used, I'm crossing them out. So I don't try to use them again. And after that, I'm looking at my single cases. So without an exponent, I have a positive two K, a negative six K and a negative one K. So that when it's combined will give me a negative five K. There are no constants. So that is as simplified as it can get. So when I distribute and then combine all my like terms, I'm left with 18 K raised to the fourth power minus five K cubed plus 16 K squared minus five K. And that matches answer choice. A have a nice day.

Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) - (2m³ + 5m² + 4m) + (m² - m)

Key Concepts

Polynomial Addition and Subtraction

Like Terms

Distributive Property

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