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

Question

Accepted Answer

Hello today we're going to be performing the indicated multiplication. So what we are given is the quantity four A plus five times the quantity negative a squared plus five a minus six. Now in order to perform this multiplication, we're essentially going to need to foil both of the quantities together. So in order to foil the quantities we're going to take the first term for A and multiply to the three terms in the second quantity. So to start that process for a times negative A squared is going to give us negative four A cubed next four a times five A is going to give us positive 20 A squared Next four A. Times negative six is going to give us negative 24 A. Now we're going to foil the second term of the first quantity with each term in the second quantity. So five times negative A squared is going to give us negative five A squared Next five times 5 a. is going to give us positive 25 a And finally five times negative six is going to give us -30. So foiling the quantities together is going to give us a product that includes a bunch of terms jumbled up together. But we can simplify this quantity by combining like terms together. So for instance we can go ahead and combine 28 squared with negative five A squared. And we can go ahead and combine negative 24 A with positive 25 A. So we're gonna first start by writing the simplified form with negative for a cubed. Next we're going to write the next term with respect to the power. So we're going to write the A squared terms Next 20 A squared minus five A squared is going to give us positive 15 A squared. Next we're going to write the A. Terms and negative 24 A plus 25 A is just going to give us positive A. Finally we write down our constant that's left over, which is going to be negative 30 and this is going to be the product of the two quantities in its simplified form. And with that being said, the answer to this problem is going to be C. 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. (3w+2)(-w^2+4w-3)

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