How to Do Distributive Property & Combine Like Terms

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Part of the distributive property is combining like terms within a problem. Do the distributive property and combining like terms with help from a longtime math teacher in this free video clip.

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Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to show you how to do the distributive property in combining like terms. So I'm going to give you an expression. Let's say we have 2 times the quantity of 4x plus 3, minus 3x. And I want to simplify this. So, you always distribute before you combine, so I'm going to go ahead and distribute this 2. Whenever you see a number before parentheses, it needs to distribute. So I'm going to distribute this 2 to the 4x, my first term inside of my parentheses, and to the 3, the second term inside of my parentheses. So 2 times 4x is 8x. 2 times positive 3 is positive 6. And now I'm just bringing down anything that I didn't use, which is my minus 3x. So I've distributed, and now I'm looking to combine like terms. Like terms have the same variable, same exponent, so the only like terms I see here are 8x and -3x. The most important thing about combining like terms is that you take the sign before the term, so every term has to carry the sign before it. Think of it as its little leash, okay? The 8 doesn't have one because it's the leads coefficient, but that just means that it's positive. So I'm doing 8x minus 3x, which is 5x. When you combine like terms, you only deal with the coefficients, and you keep the variables the same. And now I'm going to bring down my plus 6, because there's nothing to combine that with, and I'm done. So to distribute, you multiply the number outside of the parentheses by each number that's inside, and to combine like terms, you look for anything that has the same variable, same exponent, and these both have an imaginary 1, that's why I say some exponent. You combine their coefficients, keep their variables. My name is Marija, and I just showed you how to do the distributive property and combine like terms.

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