Question Video: Expanding an Algebraic Expression Using the Distributive Property | Nagwa Question Video: Expanding an Algebraic Expression Using the Distributive Property | Nagwa

# Question Video: Expanding an Algebraic Expression Using the Distributive Property Mathematics

Use the properties of real numbers to rewrite 6(𝑥 + 3) as an equivalent expression that does not contain parentheses.

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### Video Transcript

Use the properties of real numbers to rewrite six multiplied by 𝑥 plus three as an equivalent expression that does not contain parentheses.

In this question, we’re given an algebraic expression six multiplied by 𝑥 plus three. And we want to find an equivalent expression to this algebraic expression. However, we want this to not contain any parentheses. And we’re told that we should do this by using the properties of real numbers.

The first thing we need to do is determine which of the properties of real numbers we can use to simplify our algebraic expression. And to do this, we’re going to need to look at our algebraic expression. Since our algebraic expression involves multiplying the sum of two things, we could try simplifying this by using the distributive property of multiplication over addition. Remember, this means whenever we’re adding two numbers together and then multiplying the result, we can instead multiply each of our terms together and then add the result.

Multiplying six by the first term inside of our parentheses, we get six multiplied by 𝑥. Then remember we need to add six multiplied by the second term in our parentheses, which we know gives us six multiplied by three. Now all we need to do is simplify this expression. First, remember, we can simplify six multiplied by 𝑥 to just be six 𝑥. Next, we can evaluate six multiplied by three is equal to 18. And now we can see this is equivalent to our original expression; however, it doesn’t contain any parentheses. Therefore, this gives us our final answer.

We were able to show by using the distributive property of multiplication over addition that six multiplied by 𝑥 plus three is exactly the same as six 𝑥 plus 18.

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