Rewrite each expression using the distributive property and simpl...

Question

Rewrite each expression using the distributive property and simplify, if possible. See Example 7.

a + 7a

Accepted Answer

Welcome back, everyone. Which of the following terms refers to an atom that contains a certain number of protons and neutrons. And is used to indicate an isotope of an element. We have a nucleus b radio isotope cnu glide or D ion. Let's begin with our understanding of an atomic nuclei. So we're going to consider the following three atomic nuclei. The first is going to contain five protons and six neutrons recall that the nucleus of an atom is filled with protons and neutrons which are bound together by a strong nuclear force. So this, this nucleus specifically has five protons and six neutrons. And as a whole, we can identify this as nu Clyde one. Now we're going to have a second nu Clyde that we represent. And this new glide is going to contain five protons and seven neutrons. So it has one more neutron than the previous nu Clyde. And now we have a third new glide nu glide three, which we will represent containing six protons and six neutrons. Now focus on new glide one, sorry, new glide one which will highlight and new glide two, we highlighted these two new glides because they both contain the same number of protons being five protons. And what this means is that new glide one and new glide two are the same element again because they both have the same number of protons. However, because their number of neutrons differ, we can say that new glide one and new glide two are going to be considered isotopes because their difference is in the number of neutrons, six neutrons in new glide one versus seven neutrons in new glide two. And so we should recall that the definition of a new glide is going to be defining an individual and specific nucleus by its particular number of protons and neutrons that it contains. And an isotope is going to be a variant of an element by the differing number of neutrons. And so that is what we exemplified here, that new glide one and nu glide two are going to be isotopes of the same type of element. And that is because they have the same number of protons but differing number of neutrons. Whereas new glide three with an entire different number of protons represents a different element entirely. So let's keep in mind that all isotopes are considered new glides at their core, but not all new glides are isotopes of the same element. And that is because all new Clydes will not have the same number of protons as we saw with nu glide three, which has six protons versus nudes. One and two which both had five protons and represent isotopes of the same type of element because they have also differing number of neutrons. So I hope that that's clear. And with this understood because the prompt states that we want a term that refers to an atom defining a certain number of protons and neutrons. And used to indicate an isotope of an element will place a check mark by choice CNU glide because that would make sense based on what we covered. But now let's consider choice B radio isotope. Let's recall that a radio isotope is a term used to describe an unstable nucleus. And this unstable nucleus is going to be prone to undergo spontaneous decay because it is unstable and it will undergo spontaneous decay to become more stable and will also trigger the release of radiation via electromagnetic particles or waves. And so, because this has nothing to do with defining a atom with a particular number of protons and neutrons nor is radioisotope. A term used to indicate an isotope of an element. We're going to rule out choice B. Now we have choice D ion to consider, let's recall a poly atomic ion such as carbonate co three with a two minus charge. And this negative charge of minus two indicates that this is an anion with a negative charge. And let's also think of a positively charged ion such as silver, which is a group, one, a sorry group, one B atom on the periodic table in the D block of our periodic table where we have the transition elements. And silver is an exception in the transition metal group because it only typically will always have this plus one cat charge as an ion. So this positive plus one charge means it is a cat. And in total, we can consider both carbonate and silver caron as ions. So that does not tell us about the number of protons in neutrons contained in these atoms. Nor does this term ion indicate an isotope of an element. And we will rule out choice D for that reason. And now we have a nucleus and nucleus is again the core of an atom that contains the protons and neutrons bound together by the strong nuclear force. So nucleus is the general term to describe just the core of an atom around which negatively charged electrons will orbit on the outside. This is not going to be the right term to use to answer this prompt because again, we want to use the term new Clyde. So a we will rule out as an answer choice and that allows us to confirm that it is choice c the term new glide, which is the right term to use to describe an atom containing a certain number of protons and neutrons and used to indicate an isotope of an element. So this would be our final answer. I hope this makes sense and let us know if you have any questions.

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. a + 7a

Key Concepts

Distributive Property

Combining Like Terms

Simplification of Algebraic Expressions

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