An Intro to Combining Like Terms | Simplifying Expressions by Combining Like Terms | Math with Mr. J (2023)

Introduction

Welcome to An Intro to Combining Like Terms with Mr. J! Need help with simplifying expressions by combining like terms? You're in the right place!

Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with how to combine like terms. Mr. J will go through examples of simplifying expressions and explain how to combine like terms.

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Content

Welcome to math, with Mr Jay in this video I'm, going to go through an introduction to combining, like terms now remember like terms, are terms with the same variables to the same Powers.

When we combine like terms, we look for any like terms in the given algebraic expression and combine them into one term.

By combining like terms, we can simplify expressions.

That just means we can rewrite the original expression in a simpler and easier way to understand and work with, let's jump into number one where we have 9x plus 3x.

We will start with this basic expression and work our way up.

So we have two terms in this expression: 9x and 3X.

Both terms have the same variable of X, and these variables of X are to the same power.

Remember when we don't have an exponent attached to a variable.

There is an understood exponent of one anything to the power of one is just itself so 9x and 3X are like terms now.

When we combine like terms all we need to do is add or subtract the coefficients, the numbers in front of the variables, the coefficients in number, one are nine and three: we have a positive 9x, plus a positive 3x.

So, let's add those coefficients.

Nine plus three is twelve, and then we have the variable of X and that's it.

We took those two like terms 9x and 3X, and combined them into one term.

12X 12x is equivalent to 9x plus 3x.

So we didn't change the value of the expression.

So 12x is our final simplified expression.

Let's move on to number two where we have 8G, plus seven plus five G plus 2.

r.

Are there any like terms that we can combine in order to simplify this expression? Yes, we have 8G and 5G both of those terms have that variable of G, and then we have constant terms, seven and two I'll box in the constant terms to separate them from The 8G and the 5G.

Now we can combine like terms we have 8G plus 5G, that gives us 13 G, and then we have 7 plus 2.

That gives us nine, so we end up with 13, G plus nine, and that's our simplified expression that expression of 13 G, Plus 9, is equivalent to the original expression.

We were just able to simplify the original expression by combining like terms, we started with four total terms, but we were able to combine like terms and now we only have two total terms.

Let's move on to number three, where we have six y squared, plus 10y, plus two y squared plus 3y plus y.

Let's find any like terms that we can combine we'll start with 6y squared 2y squared is a like term.

Both of those terms have that variable of Y to The Power of 2.

Now.

Do we have any other like terms within this algebraic expression that we can combine? Yes, 10y and I will box these terms in in order to separate them from the Y squared terms, 3y and then y now.

I do want to mention this term right here, the Y, the variable by itself.

The coefficient is one: we don't have a coefficient written in front whenever you see that the coefficient is one.

There is an understood one in front of a variable and it can be helpful to write that one in there when you combine like terms so you can always write that one if you would like now, since this algebraic expression has five terms and we are working our way up to more complicated algebraic expressions, we're going to use a strategy to help us organize the expression before we combine like terms we are going to rearrange and rewrite the expression and put the like terms next to each other, I'll start with 6 y squared plus the like term of 2 y squared plus.

Now we have the Y terms, so 10y plus 3y Plus 1y.

So now all of the like terms are next to each other and it's a little easier to see what we can combine.

So this is a strategy to keep in mind now.

Do you have to do this step in order to combine like terms no, but it can be helpful now we can combine like terms we will start with 6y, squared plus 2y.

Squared so add the coefficients.

Six plus two is eight, and then we have y squared Plus.

Now we can combine the Y terms, so we have ten plus three plus one.

Ten plus three is thirteen.

Plus one is fourteen, so we get eight y squared plus fourteen Y and that's the simplified expression.

We now have an equivalent expression that is simpler than the original We simplify the expression.

We went from five terms to two terms: let's move on to number four, where we have seven X, plus two y minus 4X, plus 2y.

Let's find any like terms that we can combine, we will start with 7x and negative 4X.

Now, when we combine like terms a term, is going to take the sign, that's in front of it, so this is negative 4X.

Then we have 2y and 2y.

So, let's box those terms in in order to separate them from the X terms.

Now we can rewrite this expression with the like terms.

Next to each other, we will start with 7X minus 4X, so we have a negative 4X.

There make sure to bring the sign that's in front of the term with it when we rewrite the expression plus 2y.

So now we have the Y terms Plus another 2y.

Now we can combine like terms so we have 7x minus 4X, or you can think of this as 7x being combined with negative 4X.

However, you want to think about it.

7 minus 4 is 3, and then we have the x or, if you're thinking about it as 7x, combined with a negative 4X, 7 and negative 4, give us 3 as well.

Then we have our 2y plus 2y.

That gives us plus 4y.

So we end up with 3x plus 4y and that's our simplified expression.

We went from four total terms to two total terms by combining, like terms 3x plus 4y is equivalent to the original expression.

We were just able to again simplify this expression by combining, like terms terms now, I also want to go through simplifying this expression, a slightly different way to start off and that's by rewriting the original expression, with only addition separating the terms.

We do this by changing any subtraction to adding the opposite.

The benefit of having all terms separated only by addition is that it's a little simpler to identify all of the terms, especially any negative terms.

It kind of organizes the expression and helps any negatives stand out.

I'll rewrite the expression off to the side here so 7x, plus 2y minus 4X, plus 2 y.

So let's rewrite subtraction as adding the opposite.

So adding the opposite of a positive 4X is a negative 4X.

So adding the opposite: let's rewrite the expression with that change, so we have 7x, plus 2y, plus negative 4X, plus 2 y.

Let's rewrite that expression with like terms next to each other, so 7X Plus, negative, 4X, Plus, 2y, plus 2 y.

Now we can combine like terms we have 7X, plus negative 4X that gives us 3x and then we have 2y plus 2y, so that gives us Plus 4y, 3x plus 4y.

That way as well.

So that's just another strategy to be aware of so there you have it there's an introduction to combining, like terms I hope that helped thanks so much for watching until next time, peace.