Find each product. See Examples 3–5. (2z-1)(-z^2+3z-4)

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Accepted Answer

Hello Today we're going to be performing the indicated multiplication. So what we are given is the quantity seven x minus five times the quantity negative two X squared plus six X minus nine. Now in order to multiply these quantities together, we're essentially going to need to foil them together. So in order to start the foil we're going to take the first term of the first quantity seven X. And multiply to the three terms in the second quantity. So to start that process we're going to take seven X. And multiply it to negative two X squared. So seven X times negative two X squared is going to give us negative X cubed. Next seven X times six X is going to give us positive 42 X squared next seven X times negative nine is going to give us negative 63 X. Now we're going to repeat this process with the next term in the first quantity which is going to be negative five. So negative five times negative two X squared is going to give us positive 10 X squared. Next negative five times positive six X. Is going to give us negative 30 X and negative five Times -9 is going to give us positive 45. So what we have here is the product of the two quantities. However, we can go ahead and simplify this by combining the like terms together. So for instance we can go ahead and combine the X square terms together. So we can combine 42 X squared with 10 X squared. And we can also combine negative 63 X with negative 30 X. And we're going to rewrite the simplified form with respect to the exponents. So the simplified form is going to start with negative 14 X cubed. Next we're going to combine the X squared terms and 42 X squared plus 10 X squared is going to give us positive 52 X squared. Now we're going to write the X term and negative 63 X minus 30 X is going to give us negative 93 X. Finally we're going to write down our constant which is positive this is going to be the product of the two quantities simplified and with that being said, the answer to this problem is going to be be so I hope this video helps you in understanding how to perform this multiplication and I'll go ahead and see you all in the next video.

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Find each product. See Examples 3–5. (2z-1)(-z^2+3z-4)

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