### Video Transcript

Letโs take a look at how we
evaluate simple algebraic expressions. Algebra is the branch of
mathematics that deals with variables. And a variable is a symbol that
represents an unknown quantity. But those are all just words. Letโs look at some examples.

๐ plus three. In this expression the letter ๐ is
the variable. This ๐ represents an unknown
quality, an amount that we donโt know. An ๐ plus three together is an
algebraic expression. Itโs algebraic, or from algebra,
because this expression ๐ plus three contains a variable; it contains ๐.

And itโs an expression because it
contains a number or numbers and at least one operation. So, here, we have the operation of
addition and the number three to make this an expression. ๐ plus three is an example of an
algebraic expression. But remember our goal is solving
algebraic expressions. So, in order to do that, weโre
going to need a little bit more information. Here is our extra information.

Evaluate ๐ plus three if ๐ equals
five.

My first step here is just to copy
down exactly the expression ๐ plus three. Our next step is to replace the ๐
with a five. After that, I add five and
three. And I understand that ๐ plus three
when ๐ equals five is eight. So, weโve evaluated, or solved, our
expression ๐ plus three with the given information.

Letโs take a look at this
example.

Solve for the expression below if
๐ equals seven and ๐ equals five.

Our expression is eight plus ๐
minus ๐. We just need to start by copying
down the expression exactly how itโs listed in the problem. Then, I wanna replace ๐ and ๐
with their corresponding values, in this case ๐ being equal to five and ๐ being
equal to seven. Now, I have an expression thatโs
full of numbers and I can follow the order of operations.

Iโll add eight and five to give me
13. I added the eight and five first
because in the order of operations we want to add and subtract from left to
right. And finally, weโll subtract the
seven from the 13, which equals six. When weโre given these values for
๐ and ๐, when weโre given ๐ equals seven and ๐ equals five, we can understand
that eight plus ๐ minus ๐ equals six.

Remember how I said earlier that
algebraic expressions contain at least one operation. So far, weโve only seen examples of
addition and subtraction in expressions. But expressions can also contain
multiplication and division. In fact, hereโs an example of an
algebraic expression with multiplication. Are you curious how this is an
example of an expression with multiplication? Five ๐ equals five times ๐. In algebra the multiplication sign
is often omitted. You might see something like nine
๐ , three ๐๐, or even ๐ง๐ฆ. Nine ๐ is the same thing as saying
nine times ๐ . Three ๐๐ equals three times ๐
times ๐. And ๐ฆ๐ง equals ๐ฆ times ๐ง.

Now, I want you to take a look at
the numbers that Iโve highlighted in green. In algebra thereโs a special name
for these numbers that are being multiplied by variables. These numbers are called the
coefficient. Coefficient is a factor of a
multiplication expression. Hereโs an example of a
multiplication expression.

Evaluate seven ๐ค if ๐ค equals
four.

First, copy down the
expression. Next, Iโm gonna replace my ๐ค with
the four. And I also added a multiplication
symbol in this time. After that I multiply seven times
four. The solution to this expression is
seven times four, which is 28.

Hereโs a slightly harder
example.

Evaluate ๐ฆ squared minus four plus
three if ๐ฆ equals six.

Even though this expression has
three different operations, we always start with the same procedure. Iโm sure you guessed copy down the
expression. And if you did, you would be right;
thatโs the first thing we need to do. Next, weโre gonna replace ๐ฆ with
six because that was our given value. As you solve more and more
complicated expressions, the most important thing you can remember is that you have
to follow the order of operations.

We have correctly substituted the
six for the ๐ฆ. But now, what operation comes
first? Since we donโt have any parentheses
or brackets in this problem, order of operations would tell us to go ahead and solve
your exponents next. So, Iโve solved for six squared
which equals 36 and copied the rest of the problem down. Following order of operations, I
now need to add and subtract from left to right. In this step, I subtracted four
from 36. And our next order of operations
step will be to add 32 plus three. Our final answer for this
expression when ๐ฆ equals six, ๐ฆ squared minus four plus three equals 35.

Okay, so letโs review. The first thing that weโll do when
weโre trying to evaluate algebraic expressions is to substitute given values for the
variables. And after that, you need to be very
careful to follow the order of operations to evaluate each operation thatโs in your
expression. The best way for you to get good at
evaluating expressions is to try it and then practice. So, now, itโs your turn.