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.

(√2x - √y)²

Accepted Answer

Hello, today we're gonna be simplifying the given expression. So what we are given is the quantity, the square root of five M minus the square root of N that quantity squared. Now, since the quantity is squared, that means that there are at least two instances of this given quantity. So we can expand the current expression and write it as the square root of five M minus the square root of N multiplied by the square root of five M minus the square root of N. And now, in order to simplify this quantity, we're going to have to foil the two quantities together. So we're going to distribute the first term of the first group to each term in the second group. The square root of five M times the square root of five M is going to simplify to give us the square root of five M squared. Then the square of five M minus times negative square root of N is going to give us the negative square root of five M multiplied by the square root of N. Then we're going to repeat this process of distribution to the second term in the first group and distribute it to each term in the second group. So the negative square root of N times the square root of five M is going to give us the negative square root of five M multiplied by the square root of N and negative square root of N times negative square root of N is going to give us positive square root of N squared. Now there's a bit of simplification that we can do here. The exponent of two inside of the square root is going to allow us to cancel out the square root symbol. And we can go ahead and cancel out the square root with the first term and the last term. So the first term is going to simplify to give us five M and the last term is going to simplify to give us N. Furthermore, we can go ahead and combine the middle two terms by adding the coefficients together and the negative coefficient minus another negative coefficient is going to give us negative two times the square root of five M times the square root of N. And we can further simplify these square roots by combining the inside product. And we can rewrite this term as negative two times the square root of five M N. So now if we combine all of the terms together, what we are left with is five M minus two times the square root of five M N plus N 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 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.

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

Key Concepts

Binomial Expansion

Radical Expressions

Simplification of Expressions

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