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.

(4 + √5) (10 - 3√5)

Accepted Answer

Hello everyone. For the following expression, we will perform multiplication and simplify if possible. The expression we're given is the Kandi 11 plus radical 29 multiplied by the Kandi 17 minus 7 Radical 29. Our answer choices are a negative 16 -60 radical B 16 -60 radical C si negative 16 plus radical 29 D 16 plus 60 radical 29 rewriting my multiplication. I again have the quantity of 11 plus the square root of 29 multiplied by the quantity -7 Radical 29. I'm gonna treat this like I would treat any binomial. I was asked to multiply I'm gonna use foil. So in foil, my first terms get multiplied together. So 11 multiplied by Is 187. Then outer 11 multiplied by -7 radical 29. We're gonna multiply our coefficients and leave the radical alone. So this will be a minus or negative 77 radical 29, inner Radical 29 multiplied by 17. So that's plus 17 radical 29. So we can treat our radical just like we would if it was a variable and last the square root of 29 multiplied by negative seven square root of 29 they'll give us negative seven and that's still got the square root. And now I'm gonna put it under there as 29 squared. So recall that when you multiply radicals, you keep the sign, you multiply what's underneath 29 multiplied by 29 is the same as 29 squared. I'm writing it that way instead of multiplying it out to make it simpler to combine like terms in the next couple of steps. So in my next step, I will be combining whatever like terms I can or simplifying whatever radicals I can. So 187 stays put negative 77 radical 29 plus 17 radical 29 I can combine those because they have the same radical and that will result in negative 60 radical 29. In my last term, I have -7, but I can clean up the square root of 29 squared, a square and a square root are opposites of each other. So the square root of 29 squared is 29. This will need to be multiplied by our seven because seven was multiplied by the radical. So we will do that in our next step. So right now I have -60 Radical 29. And I'm gonna find out what negative seven multiplied by 29 is and it appears to be 203. So -203. So now I have one last set of like terms to combine, I need to combine the 187 and the -203. And when I combine those, I end up with a negative -60 Radical 29. And that is my solution and that matches answer choice a again, negative 16 -60 radical 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. (4 + √5) (10 - 3√5)