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### Course: Algebra (all content) > Unit 1

Lesson 8: Combining like terms- Intro to combining like terms
- Combining like terms with negative coefficients & distribution
- Combining like terms with distribution
- Combining like terms with distribution
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients & distribution
- Combining like terms with rational coefficients
- Combining like terms with rational coefficients
- Combining like terms review

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# Combining like terms with distribution

Learn to expand and simplify an expression like 3(5x+6) + (7x+2)*4.

## Want to join the conversation?

- Does anyone know a faster way of combining like terms(10 votes)
- How would I do this?

8(a+2)+2(2+3a)(4 votes)- First you would take the first brackets and multiply them by eight , 8*a = 8a, 8*2 = 16

now keep 8a and 16 aside

lets go to the next bracket(2(2+3a))

and multiply them by two

2*2 = 4 and 2*3a = 6a

now lets keep them aside too

now lets take them both and keep them in a equation:-

8a + 16 + 4 + 6a

then lets get the like terms together

8a + 6a + 4 + 16

now add 8a + 6a this is the same thing as adding

6 to 8 so lets add them in which you get

14a

now lets keep it aside then lets add 14 + 6

which is 20

now lets get our 14a and 20 and form a equation:-

14a + 20

so the answer is

14a + 20(4 votes)

- it is not that confusing when you got the hang of it(3 votes)
- what is 3(5x+6) + (7x+2)*4.(2 votes)
- Why don't you give it a try.

1) Eliminate the 1st set of parentheses by multiply 3 with both the 5x and the +6.

2) Eliminate the 2nd set of parentheses by multiplying 4 with both the 7x and the +2

3) You will now have 4 terms. Combine the like terms. Your answer should have 2 terms.

Give it a try. Comment back if you want to check your result.(1 vote)

- So we always have to do the first number. Ex 3(5x+6) like that(2 votes)
- is there any other methods?(2 votes)
- how do i do this (2+2w)⋅4+9(w+3)(2 votes)
- What if I have (3+2y)⋅8-10? do I distribute both the 8 and 10 to the 3 and 2? or do I just do the 8 into the 3 and two?(1 vote)
- You multiply the 8 with (3+2y), and only after that add 10.(2 votes)

- At1:56can you do a video on expressions with just one digit with a variable. I just ran into a question like that and didn't understand what was going on.(1 vote)
- How does it work if you have fractions?(1 vote)
- The process is the same. Identify the like terms and then add/subtract their coefficients. Make sure you follow the steps needed to add/subtract fractions. Find & convert the fractions to a common denominator before adding/subtracting.

You can find a video later in this lesson at: https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/alg-manipulating-expressions/v/simplifying-expressions-involving-rational-numbers(1 vote)

## Video transcript

- [Voiceover] So I have
an expression here. Three times the entire
expression 5x plus six, and then plus the expression 7x plus two and all of that times four. And what I encourage you
to do is pause this video and see if you can
simplify this expression. And I'll give you a hint. You're gonna have to do some distribution and then some combining of like terms. All right, now I'm assuming
you've had a go at it. Now let's work through this together. So as I mentioned, when
I see this three times the entire expression 5x plus six, I want to distribute that three. So I want to multiply that three times 5x and that three times the six. So three times 5x, well if I have five Xs and I have three times
that, I'm gonna have 15 Xs. And then three times six is 18. So this part of the expression
we have now simplified to 15x plus 18. Now let's do the next part. So here I have this larger
expression written before this four but I wanna do the same thing. I just wanna distribute the four. It doesn't matter whether I'm multiplying, if I have the three or if I
have the number on the left side or the right side, so
let's distribute this four. I wanna do four times 7x and
I wanna do four times two. Four times 7x, well
that's going to be 28x, 28x. And then four times two
is going to be eight. So we're almost there. This part of our expression has
simplified to 28x plus eight and now we can combine similar terms. So we have 15 Xs, and then we can add that to 28 Xs. Let me do this in a different color. If I have 15 of something
and I add 28 of something of that same something to it, well then I'm gonna have what, 43 Xs. So 43 Xs. 15x plus 28 Xs, I added
the coefficients there, that's gonna be 43 Xs. And then 18 plus eight. Hey, let me do this in a new color. So 18 plus eight is going to be 26. And we're done. We've simplified this longer expression. We did some distribution then we combined some terms to get 43x plus 26.