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(male narrator) In this video,
we're going to take a look
at how we can simplify algebraic expressions
by distributing and combining like terms.
Order of operations tells us that multiplication...
comes before addition.
This means we must follow the same pattern to simplify
by distributing and combining like terms.
We will always distribute first...
which is our multiplication step,
and then combine like terms...
last.
Let's take a look at some examples
where we do just that--
distribute and combine like terms.
In this problem, you notice there is a 4
in front of the first set of parentheses.
We'll start by distributing that 4 through the parentheses:
4 times the 3x comes first.
That's 12x.
Four times the -7 is -28.
You will also notice that there's a -7
in front of the second parentheses.
We'll distribute that as well and take careful note
of the negative that comes with the 7.
Multiplying -7 by 2x is -14x.
Again, multiplying -7 times a +1 gives us -7.
We are now done distributing.
After distributing,
we will always check to combine like terms.
Notice the 12x is like the -14x: 12 minus 14 is -2 of these x's.
Also, -28 is like the -7: -28 minus 7 is -35.
And that will complete our problem.
We cannot combine the 2x and the 35,
because they are not like terms.
Let's try another example where we are asked
to distribute and combine like terms.
In this problem, notice we have a 2
in front of the first set of parentheses.
Let's start by distributing that 2 through:
2 times 7x is 14x; 2 times the -3 is -6.
Notice the second part has just a minus sign and no number,
but it is important to recall
that if we see no number written in front of something,
in algebra, we can always assume
that the number 1 is actually in front.
This actually means
we're distributing -1 through the parentheses:
-1 times 8x is -8x.
Again, -1 times 9 is -9.
Now that we've done the distributing,
we're ready to combine like terms.
The 14x is like the -8x, both have an x:
14 minus 8 is 6.
We have 6x.
Also, we have -6 and -9, which is -15.
And this completes our problem.
We cannot combine the 6x and the 15,
because they are not like terms.
By remembering to distribute first and combine second,
we can simplify several more algebraic expressions.