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(male narrator) In this video,
we're gonna take a look
at simplifying algebraic expressions
by doing what's called "combining like terms."
First, we need to know what a term is.
Terms are when we have variables...
and/or numbers...
multiplied...
together.
For example, we might see 5a squared, b--
numbers and variables multiplied together.
Another example of a term might be ac squared.
No number required.
In fact, we don't even need a variable.
Six is also considered a term.
When we say we have "like terms,"
what we're saying is that the variables...
and exponents...
match.
And what's special
about when the variables and exponents match
is we can combine like terms.
When we have like terms, we can add...the coefficients--
that simply means the number in front...
of the like terms.
Let's look at some examples where we can find like terms
and add the coefficients or numbers from the like terms.
In this expression, we see lots of different types of terms.
Notice the terms are separated by either a plus or a minus.
Terms are always added and subtracted together.
The first term is 4x cubed.
There's another term just like it--the 5x cubed.
Notice the variable and exponent match,
so we can add the numbers in front:
4 plus 5 gives us 9 of these x cubes.
Next, there's a -2x squared.
Notice the negative stays with the number.
The other x squared-- the like term--is -4x squared.
Adding the coefficients, -2 and -4 is -6x squared.
Similarly, we can combine the x's:
2x is like the -6x; 2x minus 6x is -4x.
And that completes this problem.
We cannot combine the 9, 6, and 4,
because they are not like terms.
The exponents do not match.
This is our solution.
Let's try another problem
where we combine like terms to simplify the expression.
Here, we start with a 4y.
The term like it is the -6y: 4y minus 6y is -2y--
combining the numbers or coefficients in front.
Here, we have a -2x.
The -2x can be combined with the like term 7x:
-2 plus 7 is +5x.
Finally, the plus 5 has no variables on it.
That is like the minus 9 that also has no variables on it:
5 minus 9 is -4.
And that completes this problem.
We cannot combine the -2, 5, and -4,
because they are not like terms.
The variables do not match.
This is our solution.
As we simplify our algebraic expressions,
combining like terms--
when the variables and exponents match--
will help us achieve our solution.