Combining Like Terms and Distributive Property: Algebra

Greetings math peeps! In today’s post, we are going to review some of the basics: combining like terms and distributive property. It’s so important to master the basics such as these, so you’re prepared and ready to handle the harder stuff that’s just around the corner, trust me they’re coming! And for those who already feel comfortable with these topics, great! Skip ahead and try the practice questions at the bottom of this post and happy calculating! πŸ™‚

When do we combine “like terms?”

Combining like terms allows us to simplify and calculate our answer with terms that have the same variable and same exponent values only. For example, we can combine the following expression:

distributive property and combining like terms

How do we combine like terms?

We add or subtract the whole number coefficients and keep the variable they have in common.

distributive property and combining like terms
distributive property and combining like terms

Why? We could not add these two terms together because their variables do not match! 2 is multiplied by x, while 3 is multiplied by the variable xy.

distributive property and combining like terms

Why? We could not add these two terms together because their variables and exponents do not match! 2 is multiplied by x, while 3 is multiplied by the variable x^2 . Exponents for each variable must match to be considered like terms.

Distributive Property:

Combining like terms and the distributive property go hand in hand.  The distributive property rule states the following:

distributive property and combining like terms

There are no like terms to combine in the example above, but let’s see what it would like to use the distributive property and combine like terms at the same time with the following examples:

Example #1:

distributive property and combining like terms

Example #2:

In some cases, we also have to distribute the -1 that can sometimes “hide” behind a parenthesis.

distributive property and combining like terms

Try the following questions on your own on combining like terms and the distributive property and check out the video above for more!

Practice Questions:

Solutions:

Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! πŸ™‚

Looking to review more of the basics? Check out this post on graphing equations of a line y=mx+b here.

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