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### Course: Integrated math 1 > Unit 1

Lesson 5: Introduction to equivalent expressions# Equivalent expressions

In this math lesson, we learn how to find equivalent expressions by combining like terms and factoring. We start with an expression like x + 2 - y + x + 2 and simplify it by adding the x terms and factoring out common factors. This helps us compare expressions and solve problems more easily.

## Want to join the conversation?

- how should i remember order of ops (operations)?(23 votes)
- PEMDAS does really help. You can also remember it as please excuse my dear aunt sally.(63 votes)

- i see people using PEMDAS as order of operations. But what i learned was BEDMAS

Brackets

Exponents

Division

Multiplication

Addition

Subtraction

Im pretty sure it means the same thing but why does everyone have a different name for it?(18 votes)- They are the same, but the two together show some good distinctions. Brackets [] and Parentheses () both have to include the other one because you could see both. It also reminds us that division and multiplication are on the same level, so generally done left to right. Also, addition and subtraction are on the same level left to right.(13 votes)

- I still don't get it..How can I learn this without having negative thoughts about how dumb I really am?(13 votes)
- It’s important to give yourself time, understanding math concepts is a matter of effort but also patience, don’t beat yourself down because you think you can’t do it, and ask questions if you get stuck(10 votes)

- what does sal mean when he said he can factor the two out? and how did he get one from the two?(6 votes)
- Factoring is the opposite of multiplying by distribution.

For example:

Multiplication: 2(5x+1) = 2(5x) + 2(1) = 10x+2

To factor, you reverse the process. You identify the common factor in both terms (the 2), you write the 2 in front and you divide each term by 2.

10x+2 = 2(10x/2 + 2/2) = 2(5x+1)

Notice, the 2/2 = 1, that is where the 1 is coming from in the video.

Hope this helps.(20 votes)

- In this math lesson, we learn how to find equivalent expressions by combining like terms and factoring. We start with an expression like x + 2 - y + x + 2 and simplify it by adding the x terms and factoring out common factors. This helps us compare expressions and solve problems more easily.(3 votes)
- I am probably being dumb right now, but I am confused. He said that at1:41that when you factor out the 2 you get 1. Did he say that cuz 1+1=2?(2 votes)
- Not quite, it's because if you divide 2 by 2, you get 1. He was factoring out ech of the numbers by dividing them by 2. And you're not dumb, sometimes people just need a different explanation.(23 votes)

- When he factors out the 2, he gets 1. I don’t quite understand how you got 1 by factoring out the 2!(3 votes)
- If you factor 2 from 2, you are dividing 2/2=1(17 votes)

- why do you have a 1 left over at1:42?(6 votes)
- When you multiply 2 by x and 2 by y and 2 by 1 you get 2x+2y+2. I hope that helps.(4 votes)

- Is a number with multiple letters accountable? (2jkl).(5 votes)
- What matters is the idea of a common factor , if you have:

2kjl +4kj +2 you can still factor this as : 2(kjl + 2kj +1) the expressions are still equivalent(3 votes)

- Wow,ok how about 15x+4+y+5(4 votes)
- In this case you can’t make any useful factorizations, notice that to factor an expression, every argument should in this case be a multiple of 5 in order to factor out a 5(2 votes)

## Video transcript

- Which expressions are equivalent to x plus two-y plus x plus two? Select all that apply. Alright. Let's see if I can manipulate
this thing a little bit. Let me just rewrite it so I have x plus... x plus two-y plus x plus two. So, the first thing that jumps out at me, before I even look at these choices, here I have an x over here,
I have an x over there. Well, if I have one x, and
then I can add it to another x that would be two-x so
I could rewrite this... let me do this in a different color. I could rewrite this x and this x, if I add them together
that's going to be two-x. So, this is...actually, I
don't want to skip any steps. So, that's x plus x plus two-y... now I'm just switching
the order...plus two. And then these two x's right over here, I can just rewrite that as two-x. So, I have two-x plus two-y... plus two-y plus two. Now, let's see, out of all my choices... so, this one, this is two-x plus four-y plus four. So, that's not right, I have
two-x plus two-y plus 2, so I can rule this one out. Now, this one's interesting, it looks like they have factored out a two. Let's see if we factor out
a two here, what happens? So, we do see that two
is a factor of that term, it's a factor of that term,
and it's a factor of that term. So, let's see if we can factor it out. So, this is going to be two times x, I'll do the x in that same
magenta color, two times x plus, we have just a y left when
you factor out the two. And then if you factor out a two here, you're just going to have a one left. So, two times x plus y plus one. Which is exactly what they have over here. And since I was able to find a choice, I will not pick "None of the above".