In Exercises 1–20, use the product rule to multiply.___ ___√x+6 ⋅...

Question

In Exercises 1–20, use the product rule to multiply.___ ___√x+6 ⋅ √x-6

Accepted Answer

Hello, today we're gonna be simplifying the given expression. So what we are given is the square root of the quantity P plus eight. And we're multiplying this by the square root of the quantity P minus eight. So we have a product property that states that if we have the mth root of the A of a multiplied by the MTH root of B. As long as the outside numbers in front of the square root symbols are exactly the same, then we can simplify this by combining the product of the inside arguments into a single square root. And we can rewrite this product as the mth root of A times B. So if we apply this property to the given expression, notice that both of the square root symbols are exactly the same. Thus, we can combine this into a single square root and rewrite the expression as the square root of P plus eight multiplied by the quantity P minus eight. And now we need to simplify the inside argument. And in order to do that, we're going to need to foil the two quantities together. So we have the quantity P plus eight multiplied by the quantity P minus eight. So in order to foil these two quantities together, we're gonna multiply P with P which is going to give us P squared multiply P with negative eight which is going to give us negative eight P multiply positive eight with P which is going to give us positive A P. Then we're going to multiply eight with negative eight which is going to give us negative 64. Notice that in this expression here, we have negative A P plus eight P, combining these two terms together is going to cancel each other out. And what we are left with is P squared minus 64. So that means that the insight argument can be rewritten as the square root of P squared minus 64. And this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 1–20, use the product rule to multiply._ _√x+6 ⋅ √x-6

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