Add 6x⁴−5x³+2x to the difference between 4x³+3x²−1 and x⁴−2x²+7x−...

Question

Add 6x⁴−5x³+2x to the difference between 4x³+3x²−1 and x⁴−2x²+7x−3.

Accepted Answer

Hey, everyone in this problem, we're asked to perform the addition of the difference of eight X cubed minus two X squared plus three and 12 X cubed minus three X squared plus five with seven X to the exponent four minus two X cubed plus four X. So that's a lot. It can be confusing when we're reading math explained in words. So let's break this down and write out what we're actually trying to solve in terms of math. So we want the addition of some expressions, we want the addition of the difference of the first two expressions we were given with the last expression. OK. So we're gonna add two things together and we know that the second thing we're adding is seven X to the exponent four -2 x cubed plus 4 x. And we wanna add that to the difference of these other two expressions. So we're gonna take 8 x cubed -2 x squared plus three and subtract 12 cubed minus three X squared plus five. And that's gonna be the first part. That's what we're adding to that third expression. So now we have in math what we're trying to solve. We're given four answer choices. Option A is seven X to the exponent four minus six X cubed plus X squared plus four, X plus two. Option B seven X to the exponent four minus six X cubed plus X squared minus four, X minus two. Option C seven X, the exponent four minus six X cubed plus X squared plus four, X minus two. And option D seven X to the exponent four minus six X cubed minus X squared plus four, X minus two. Let's start in this large bracket. We have, we wanna start doing that difference and then we'll add it to the expression that we were asked to add it to. So let's start with the difference. Now, we're subtracting this entire expression of 12 X cubed minus three X squared plus five. So this minus needs to apply to every term in that expression. So let's go ahead and expand inside of our brackets and distribute that negative to all of those terms. We have 8 x cubed -2, x squared plus three -12 x cubed plus 3 x squared minus five. And all of this is added to the expression seven X to the exponent four minus two X cubed plus four X. Now if we look in our first where we did our subtraction or where we're doing our subtraction, you can see in this second part of the expression, the values that were originally positive are now negative and being subtracted like 12 X cubed and five, the values that were originally negative three X squared are now positive. OK. That's because we're subtracting the entire expression. So we have a negative times a positive value gives us a negative value. A negative value times a negative value gives us a positive value. OK. So we're getting closer. Let's continue to simplify and work out this difference in our first set of brackets before we add it to the second expression and we're gonna collect light terms. So starting here, we have an XQ term 8 XQ. Do we have any other X cube terms? Yeah, we have negative 12 X cubed, 8 x cubed -12 x cubed gives us -4 execute. And we move to our next term. Our next term is minus two X squared. We also have a three X squared term negative two X squared plus three X squared gives us plus X squared. In our expression, we have plus 3 -5 in our expression. This is going to give us -2. OK. So those constant terms getting simplified and now we've dealt with every term in our original expression. That first part, we have negative four X cubed plus X squared minus two. And that's gonna be added to the second expression seven X to the exponent four minus two X cubed plus four X. And now we wanna do the same thing. We want to take our like terms and combine them. We're gonna start left to right, just like we did before negative four X cubed. And do we have any other X cube terms? Yeah, we have negative two X cubed, negative four X cubed minus two X cube gives us negative six X cubed. We have plus X squared. We don't have any other X squared terms. And so we're gonna have plus X squared -2. We don't have any other constant terms. We keep -2 plus seven X to the exponent four. We don't have any other terms with an exponent of four. So we have plus seven X to the exponent four. We've already accounted for this -2 XQ term. And then we have plus four X, our final term. So plus 4 x now we've done the simplification. We've got all of the terms that we needed. We're just gonna rearrange in our answer choices. They're arranged from the highest exponent all the way down to the constant term from left to right. So we're gonna arrange our expression in the exact same way so that we can compare it more easily. So our highest exponent is four. So we're gonna write that term first seven X to the exponent four, then our X cube term -6 x cued plus X squared plus four, X minus two. And this is the resulting expression that's been simplified when we perform the addition and subtraction that we were asked to perform in the problem comparing this to our answer choices. We found the result is seven X to the exponent four minus six X cubed plus X squared plus four X minus two, which corresponds with answer choice. C thanks everyone for watching. I hope this video helped you in the next one.

Add 6x⁴−5x³+2x to the difference between 4x³+3x²−1 and x⁴−2x²+7x−3.

Key Concepts

Polynomial Addition

Polynomial Subtraction

Combining Polynomials

Watch next