WEBVTT
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Hi, this is Anthony Varela.
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And today, we're going to
talk about terms and factors
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in algebraic expressions.
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So we're going to look
at different types
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of algebraic expressions.
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And then we're going to
look at the components that
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make up algebraic expressions.
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And then we're going to
practice combining like terms
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in algebraic expressions.
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So let's start out by an example
of what an algebraic expression
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might look like.
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So here we have 3x squared.
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This is an algebraic expression.
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So an algebraic expression
is a combination
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of numbers, variables,
and operators
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representing a quantity.
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So here, I see the number 3.
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I see the variable x.
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I see x being raised
to the power of 2.
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So that's an operation here.
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And this contains a variable.
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So a variable is a
quantity that can change.
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And it's expressed as
a letter or a symbol.
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So here we have the variable x.
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And we see that x is being
multiplied by itself.
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And then it's being
multiplied by 3.
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And those are all
what we call factors.
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And a factor is a
number or quantity
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used in multiplication.
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So this is made up
of the factor 3.
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And then we have
two factors of x.
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And 3x squared is an algebraic
expression containing one term.
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And a term is a collection of
numbers, variables, and powers
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combined through multiplication.
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So since all of these are
being multiplied together,
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this equals one term.
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And we call an algebraic
expression containing
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only one term a monomial.
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So mono equals 1.
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So a monomial is one term.
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Well, let's take a look
at 3x squared plus 7.
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And we call this algebraic
expression a binomial.
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It has two terms.
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One term is 3x squared.
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And the other term is 7.
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So let's talk more
about these two terms.
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Well, we have a constant term.
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And this is a term with
no variable component.
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So this is a constant.
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There are no variables that are
being attached to this term.
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Now we also have a coefficient
in our x squared term.
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And this is the number in front
of a variable term that acts
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as a factor or a multiplier.
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And so we should note also that
we talk about these terms using
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their variable power.
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So this 3x squared term, we
call it the x squared term.
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We call it that because
we see the variable x.
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And x is raised
to the power of 2.
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So 3 is a coefficient
to the x squared term.
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7 doesn't have a
variable component,
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so we call that a constant.
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Well, here is another
algebraic expression.
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And this is made up of
one, two, three terms.
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So we could call it a trinomial
because it has three terms.
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But we can also say that
this is a polynomial.
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It's an expression
containing several terms.
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So it's not a monomial because
it has more than one term.
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It's not a binomial because it
doesn't have exactly two terms,
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but it's a polynomial.
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It has several terms.
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And let's go ahead
and identify then
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the terms, constants,
and coefficients
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in this algebraic expression.
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So remember, a term, we're
looking for numbers, variables,
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and powers that
are all connected
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through multiplication.
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So here is a term.
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Here is a term.
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And here is a term.
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Notice that they're separated
by addition or subtraction.
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So our terms here are
3x squared, 5x, and 7.
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So notice we have
an x squared term.
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We have an x term.
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And then we have a constant
term, no variable at all.
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So that leads us into
our next category here.
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What are the constants
in this expression?
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Well, we just have one constant.
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That would be 7 because there's
no variable component there.
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Now do we have coefficients?
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Remember, coefficients
are the numbers
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that are in front of our
variable or variable powers.
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So we have two coefficients--
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3 and 5.
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3 is the coefficient
of our x squared term.
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5 is the coefficient
of our x term.
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So there are the terms,
constants, and coefficients
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for this expression.
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Now let's talk about
combining like terms.
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So let's take this
expression as an example.
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We have quite a few terms here.
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There's 3x squared plus 5x
minus 2x plus 2x squared plus 2.
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So what we mean by
combining like terms--
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we're looking for terms
that have the same variable
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and the same variable power.
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So let's go ahead and
identify like terms.
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So here in green, we have
like terms because they
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are both x squared terms.
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They have different
coefficients,
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but they're both
x squared terms.
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We have another set of like
terms here highlighted in blue.
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5x and 2x are like terms
because they are both x terms.
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And then here our constant 2
doesn't have any other terms
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that are also constant.
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So that doesn't have any like
terms in this expression.
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So when we combine like
terms, what we're doing
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is adding or subtracting
the coefficients,
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depending on if they're
in a positive or negative.
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So what I'm thinking
then is I'm just
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going to be adding or
subtracting these coefficients.
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So taking a look
at our like terms
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3x squared and 2x squared, I
can just add 3 and 2 to get 5.
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And then looking at our
like terms 5x and 2x,
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I'm going to take 5 minus 2
because we have subtraction
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here and get 3.
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And these are going to be our
coefficients in our combined
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terms.
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So here's what it looks
like when you've combined
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all of our like terms--
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5x squared plus 3x plus 2.
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And once again,
I've got 5x squared
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by adding these two terms.
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I got 3x by adding
these two terms.
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And I subtracted
the coefficients
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due to this negative.
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And then I have my plus 2.
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So when we're
combining like terms
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or adding our coefficients,
and a negative coefficient then
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tells you you need to subtract.
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So let's review our notes
for terms and factors
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in algebraic expressions.
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We talked about a couple
of different algebraic
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expressions.
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We looked at a monomial
containing only one term.
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We looked at a binomial
containing two terms.
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And we saw a polynomial,
which has several terms.
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We looked at terms, factors,
coefficients, and constants
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in algebraic expressions.
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And then we talked about
combining like terms.
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So to look for
like terms, you're
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looking for the same
variable and variable
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power within a term.
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And you can combine like terms
by adding those coefficients.
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And remember, if there is a
negative coefficient, that's
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the same thing as subtracting.
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So thanks for watching this
video on "Terms and Factors
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in Algebraic Expressions."
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Hope to see you next time.