Perform the indicated operations. See Examples 2–6. -3(4q^2-3q+2)...

Question

Perform the indicated operations. See Examples 2–6. -3(4q^2-3q+2) + 2(-q^2+q-4)

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression negative five times parentheses four Z to the fourth minus nine, Z plus eight. And parentheses plus three times parentheses negative seven Z to the fourth plus 10, Z minus one. And we are asked to find the sum or essentially to add these together. But before we can do any adding, we need to distribute these numbers squished up in front of their parentheses. This negative five needs to get distributed to the three terms inside of its parentheses and the positive three needs to get distributed to the three terms inside of its parentheses. So let's go ahead and do that distribution. We're going to take negative five times four Z to the fourth. So we take the negative five times four which is negative 20 and then keep our Z to the fourth, negative five times negative nine Z. We take negative five times negative nine negative times a negative gives us a positive, so plus 45 Z - times eight is going to be a -40. Now we're distributing the 33 times negative seven Z to the fourth, three times negative seven is negative 21. Keeping our Z to the fourth, three times 10. Z. Three times 10 is 30 so plus 30. The and three times negative one is negative three. Now we need to combine like terms let's look for our Z to the fourths. We have a negative 20 Z to the fourth minus 21. Z to the fourth, combining those gives us a negative 41 Z to the fourth. Now let's look for our Z terms we have plus 45 Z. And plus 30 Z. 45 Z plus 30 Z is plus Z. And now combining our constant terms negative 40 minus three is going to be minus 43. And that's as combined as we can get them. So now we look at our answer choices. We have negative 41 Z to the fourth plus 75 Z minus 43. And that matches with answer choice C. While done, we'll catch you on the next one.

Perform the indicated operations. See Examples 2–6. -3(4q^2-3q+2) + 2(-q^2+q-4)

Key Concepts

Distributive Property

Combining Like Terms

Polynomial Operations

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