In Exercises 83–90, perform the indicated operation or operations...

Question

In Exercises 83–90, perform the indicated operation or operations. (3x+5)(2x−9)−(7x−2)(x−1)

Accepted Answer

Hello. Today we're going to be simplifying an algebraic expression. So the algebraic expression given to us is x minus five times X plus one minus two X minus three times three X plus one. So in order to start this process we're going to need to first foil together X minus five and X plus one and foil two X minus three and three X plus one. So let's go ahead and start that. So foiling X minus five with X plus one. We're going to take the first term X and multiply it with the 1st and 2nd term of the second quantity. Then we're taking our second term negative five and multiplying it with the 1st and 2nd term of the second quantity. So doing that X times X is going to give me X squared and X times one is just going to be positive X negative five times X is going to give me negative five X and negative five times one is going to give me negative five. Alright now we need to go ahead and simplifying this by combining like terms, the only combine like terms here is X and negative five X because they both have the terms X raised to the power of one combining those together is going to give me the tri no meal, X squared minus four X minus five And that's going to be X -5 times x plus one foiled together. Now we need to go ahead and foil together two X - and three X plus one. So again we're going to take our first term two X And multiply to the 1st and 2nd term of our second quantity then we're taking our second term negative three and multiplying to the 1st and 2nd term of our second quantity. So two x times three X is going to give me six X squared two x times one is going to give me positive two X negative three times three X is going to give me negative nine X and negative three times one is going to give me negative three. Now again we're going to simplify this by combining like terms and the combine herbal like terms here is two X and negative nine X. Because of the X term combining this together is going to give me the try no meal six X squared -7 X -3. Okay, now what we wanna do is go ahead and subtract the quantities from each other. So setting putting this back into our original algebraic expression is going to give us x squared minus four x minus five minus the quantity six X squared minus seven x minus three. Now we need to go ahead and open up this set of parentheses and in order to do that we're going to take the negative sign and distributed to every term in this trin Amiel doing so is going to give us x squared minus four x minus five minus six X squared Plus seven X. Because it's a negative times a negative and plus three because negative times negative is going to produce a positive. Alright now we need to go ahead and combine the like terms. Well the first set of like terms is X squared and negative six X squared, adding those together is going to give me negative five X squared. The next set of like terms is gonna be negative for X and seven X. And adding those together is going to give me positive three X. And the last set of like terms is -5 and positive three. And that's going to give me -2. And this is gonna be the simplified version of this algebraic expression. And that means that the answer to this problem is going to be a So I hope this video helps you in understanding how to simplify this algebraic expression. And I'll go ahead and see you all in the next video.

In Exercises 83–90, perform the indicated operation or operations. (3x+5)(2x−9)−(7x−2)(x−1)

Key Concepts

Polynomial Multiplication

Combining Like Terms

Distributive Property

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