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√3 + 3√2) (4√3 - 3√2)

Accepted Answer

Hello, today we're gonna be simplifying the given expression. So what we are given is the quantity six times the square root of five plus five times the square root of 17 Multiplied by the quantity six times the square root of 5 -5 times the square root of 17. Now, one trick that we can do here is to simplify this using the difference of squares, the difference of square states that if you have the binomial A squared minus B squared, this is going to factor to give us A plus B Times A. -7. And in our given expression, our expression matches the form of A plus B times A minus B. Here, we're going to let A B6 times the square root of five. And we're going to let B Be five times the square root of 17. So again, A is going to equal to six times the square root of five and B is going to equal to five times the square root of 17. And if we plug this into the form of A squared minus B squared, we can rewrite the expression as six times the square root of five squared minus five times the square root of squared. Now, what we're going to do is we're going to use our exponential distribution on both of the quantities. We're going to distribute this exponent of 2-6 and the square root of five. And we're going to distribute this exponent of 2-5 and the square root of 17. And that is going to give us six squared, which is going to simplify to 36 times the square root of five squared, which is going to simplify to just five. And we're going to subtract five squared, which is 25 times the square root of 17 squared, which is just going to give us 17. Now, we just need to go ahead and simplify from this pro from the step. So 36 times five is going to give us And 25 times 17 is going to give us 425. And finally, 180 -425 is going to simplify to give us -245. And this is going to be the simplest form of the given expression. 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 approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4√3 + 3√2) (4√3 - 3√2)