Problem

Subtract $-3 z^{3}-4 z+7$ from the sum of $2 z^{2…

03:38

Problem 67 Hard Difficulty

Subtract $t^{3}-2 t^{2}+2$ from the sum of $3 t^{3}+t^{2}$ and $-t^{3}+6 t-3$

Answer

$$t^{3}+3 t^{2}+6 t-5$$

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

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Video Transcript

this problem. We're being asked to subtract T to the third minus two t squared plus two from the some off three t to the third plus T squared in negative t to the third plus 60 minus tree. So the first thing we need to do is try to write an expression to represent this problem. While some of our key freezes here is, we're subtracting our first polynomial from the sum of something. Well, some means something is getting added. Well, in this case was getting added is our second and third Paulino meals. And because that first polynomial is getting subtracted from it, that actually has to go with the end. So an expression we can use to represent this sentence is we're going to do are some firsts will have the quantity of three t to the third plus t squared, plus our last polynomial, which was negative t to the third plus 60 minus three. And then we're going to subtract our first polynomial, which was negative or sorry, minus the quantity of tea to the third minus two t squared plus two. And now we simply need to combine these expressions well for the 1st 2 pollen. No meals. Since they're just being added, we just need to take each of those turns out of the preface is so, in other words will have three T to the third plus T squared minus T to the third plus 60 minus three for our last polling only because it's getting subtracted. We need to change the science of each of those terms. So whenever words that positive T to the third will become negative, teach of the third, the negative to T squared will become positive to t squared, and the positive, too, will become negative, too. And now we simply need to combine like terms. While our first term is three t to the third, it has, like terms of negative T to the third and negative teaches the third. Keep in mind when you don't see a coefficient, there's an imaginary one. So there's a one here and one here. Well, three minus one is two and two minus one is one, so we'll have one G to the third. Our next term is T squared. Well, it's like term is positive to t squared and again when you don't see a coefficient There's an Imagine Everyone, well, one plus two is equal to three, so we'll have plus three t Square. Our next term is positive. 60 and it does not have a life term, so we'll simply just bring it down for our final answer, plus 60. Next, we have negative three. Well, it's like charm is negative to both. Negative three minus two is negative five, so we can leave this as our final answer. But if you know us for our first term, it's coefficient is one. We don't necessarily have to write the one there, so we could also write our final answer as T to the third plus three t squared plus 60 minus five.

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