hey it's me kaylee are you ready to learn how to speak in algebra this lesson will give us
a lot of new words to describe what's going on in math and the world around us let's go
have you ever written an essay or a book report you might not remember it but at some point you
had to learn how to write a paragraph and before that you had to learn how to write a sentence
you learned that saying the dog is not a complete sentence because a complete sentence
needs a subject and a verb the dog is just a subject we need a verb too like barked or ran
the dog barked and the dog ran are both complete sentences now don't worry this
isn't english class but this is true in math too just like it's important to know what someone
means when they say i don't like this verb can we change it to something more action-packed
you know they're referring to barked and not the subject the dog mathematicians often work in
groups or teams and as they solve big complex math problems it's important for one mathematician to
understand the other when she says i don't agree with the fourth term or i think the coefficient
on the first term is wrong math has a common language to help us solve problems faster and
easier let's take a look at this long expression here when we come across an expression like this
the first things we want to look for are the terms or how many terms are in our expression
terms are simply the things being added or subtracted or the things that are separated
by addition and subtraction signs so how many terms do you think are in this expression
yeah that's right we have three terms right we have this one here this one here and this one here
because these are all separated by addition or subtraction signs so we could write out our terms
are 4x 10y and 14 times nine these three things are what we call terms so this expression has
three terms simple enough right now let's talk about factors the factors are the things being
multiplied together in each term so let's look at our first term what is our first term
yeah our first term is right here four x so what is being multiplied together in the first
term four and x so if we write our factors here we're going to go through each of our terms so how
many factors are in our second term our second term is 10 y what's being multiplied together
yeah 10 and y so how many factors are in our second term
yeah there's two 10 and y and how many factors are in our first term also 2 4 and x now in this
last term how many factors are there remember what does this dot or this bullet what does that mean
yeah that's right this means multiplication right so that just means multiplication so
if there's two things being multiplied together in my third term what are my factors yeah 14 and nine
so there are two factors in my third term now let's take a closer look at our first term for x
we have two factors here right 4 and x now what is the name for x why do we use a letter in algebra
that's right x is our variable and a variable is just a number that can have a different value it's
a number that is a varying value now where else in our expression here do we have another variable
another varying value so we have one here in x and do we have another one yeah this y is also a
variable now in our third term are either of these factors of varying value no we don't have any
variables here right so there's none in our third term now when we are multiplying a constant value
like this 4 here by a variable this constant value also has a special name it's called a coefficient
a coefficient is the constant value that's being multiplied by a variable
so what are the coefficients in our expression here
yeah so we know that this 4 is a coefficient because it's a factor it's being multiplied
by a variable now are there any coefficients or constant values being multiplied by a variable
in our second term are either of our factors 10 or y a coefficient yeah 10 is a coefficient and
how do we know because it's being multiplied by y and we know that y is a variable now
what about 14 and 9 are both of these numbers coefficients because they're constant values
nope actually there's no coefficients in our third term because neither of these are a variable so
even though they're constant values since they're not being multiplied by a variable we do not
refer to them as coefficients nice work here's a simple table to help you keep track of all the new
vocabulary words we've just learned these words are super important in being able to communicate
complicated formulas and equations it might be a good idea to pause the video and copy
this table down in your notebook to help you study we'll do some more examples in
the next video called parts of algebraic expression examples i'll see you there