In Exercises 55–68, multiply using one of the rules for the squar...

Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial.(2x + y)²

Accepted Answer

Hey, everyone in this problem, we're asked to perform multiplication on the given expression. The expression we're given is the binomial four M plus N squared. We have four answer choices. Option A eight M squared plus eight M N plus N squared. Option B 16 M squared plus eight M N plus N squared. Option C eight M squared minus eight M N plus N squared. And option D 16 M squared minus eight M N plus N squared. We're gonna start by rewriting what we were given. So we have four M plus N all squared. Now we can write this expression as four M plus N multiplied by four M plus N K four M plus N squared is the same thing as four M plus N multiplied by four M plus N. Now we have two binomials multiplied together, we can multiply them in any way that we typically do that. So we can use the foil method and recall that the foil method tells us to multiply the first terms, the outside terms, the inside terms. And then the last terms, if we apply this to our expression, the first term of the first binomial is four M. The first term of the second binomial is also four M. And so, for our first term, we have four M multiplied by four M and this represents the F in foil and we move, move to our next term. And the next term is given by the outside terms. So we're gonna take the two outside terms, the furthest term on the left, the furthest term on the right and multiply them together. So from the first binomial, on the very far left, we have four M and on the very far right of our expression from the second binomial, we get N, so we're gonna add to our result four M multiplied by N and this represents our outside terms or the O in foil. And now we're gonna move to our next term. Next term is the inside term. So we've just done the outside terms. Now we're gonna take the inside terms. So those two terms that sit close together in the middle, we have N from the first binomial and four M from the second binomial. So we're going to add N multiplied by four M to our expression. This represents our inside term or the I in foil, we have one more term to consider. And that's the last, so we're gonna take the last term from the first binomial, which is N and multiply it by the last term in the second binomial, which is also N. So we have N multiplied by N representing our last terms or the L in foil. Now, we've done the multiplication. We've used our foiled method. All that's left is to simplify this expression. Our first term we have four M multiplied by four M dealing with the coefficient, first four multiplied by four. It's going to give us 16 and then we have M multiplied by M to recall if we have two things multiplied together with the same base. And we can simplify them into one term where the exponents are added. So M multiplied by M gives us M to the exponent one plus one, we move to our next term 4 m multiplied by N. OK. So in our expression, we have plus four M N, our inside term is N multiplied by four M. We call it the order we multiply terms in doesn't matter. So we can rearrange this and write it as plus four M N in our last term N multiplied by N. Similarly to the rule we applied to the first term. If we're multiplying two things with the same base, we can combine them into one and add the exponents. And so we get plus and to the exponent one plus one, please simplify this expression. We have 16 M to the exponent one plus one. We can write this as 16 M squared and we have plus four M N plus four M N. So we have plus eight M N plus N to the exponent one plus one. This is gonna give us N squared. And so our resulting expression after performing multiplication and simplifying is 16 M squared plus eight M N plus N squared, which corresponds with answer choice. And B thanks everyone for watching. I hope this video helped see you in the next one.

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In Exercises 55–68, multiply using one of the rules for the square of a binomial.(2x + y)²

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