In Exercises 1–38, multiply as indicated. If possible, simplify a...

Question

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.(7 - 2√7) (5 - 3√7)

Accepted Answer

Mhm Hello everyone. For the following expression, we will perform multiplication and further simplify if possible. The expression we are given is the Kandi minus four radical 13 multiplied by the Kandi six minus five radical 13. Our answer choices are a 338 radical 13 - B 338 -89 Radical C -338 radical 13 plus D negative 338 plus 89 radical 13. We're gonna rewrite our original expression. So again, the Kandi 13 -4 radical multiplied by the Quan D 6 -5 Radical 13. And I'm gonna treat this just like I would treat any other binomial. I was asked to multiply, I'm gonna use foil. So foil again, recall is first. So 13 multiplied by 6- outer 13 multiplied by -5 radical 13. And the radical 13 is very much like a variable. So we're gonna multiply the constants and keep the radical 13 the same. So 13 multiplied by -5 is negative 65 radical 13 in -4 radical 13 multiplied by six is negative 24 radical and last -4 radical 13 multiplied by -5 radical 13 would be positive 20. And then when we multiply a radical 13 times a radical 13, you will have radical 13 squared. So we keep the radical you multiply what is under it? I rewrote it as 13 squared instead of 169 to make it simpler to combine like terms in the next couple of steps. So right now we have 78 -65 radical 13 -24 radical 13 plus multiplied by the square root of 13 Squared. I'm gonna combine my lake terms. The first lake terms I'm gonna combine are the two terms that have the radical thirteens. So negative 65 radical 13 and negative 24 radical 13 for now 78 is not gonna change. So that gets rewritten negative 65 negative 24 will combine to a negative radical 13. In my last term, I'm going to rewrite my coefficient of 20 and then simplify the square root of 13 squared. Recall that a square and a square root are opposite. So they will cancel out this leaves us with 13. So in that last term, we need to multiply 20x13 and I'm going to do that in my next step. So 78 -89 radical and now plus 20 multiplied by which is 260. Now one last set of like terms to combine and that's 78 and 260, 78 plus 260 results in -89 Radical 13. This is our solution and it matches answer choice B have a nice day.

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In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.(7 - 2√7) (5 - 3√7)

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