Question Video: Idetifying the Equation which Demonstrates the Distributive Property Mathematics • 7th Grade

Which of the following demonstrates the distributive property? [A] −4 + (𝑥 + 3) = 3 + (𝑥 − 4) [B] −4𝑥 + 3 = 3 − 4𝑥 [C] −4𝑥 + 3 + 0 = −4𝑥 + 3 [D] −4(𝑥 + 3) = −4𝑥 − 12

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Video Transcript

Which of the following demonstrates the distributive property? Option (A) negative four plus 𝑥 plus three is equal to three plus 𝑥 minus four. Option (B) negative four 𝑥 plus three is equal to three minus four 𝑥. Option (C) negative four 𝑥 plus three plus zero is equal to negative four 𝑥 plus three. Or option (D) negative four 𝑥 multiplied by 𝑥 plus three is equal to negative four 𝑥 minus 12.

In this question, we’re given four options. And we need to determine which of these demonstrates use of the distributive property. Remember when we’re using the distributive property, we need something multiplied by the sum or difference of two values. And just by using this, we can see options (A), (B), and (C) don’t contain this. There’s nothing multiplied by the sum or difference of two terms. So we could already just eliminate these three options. However, for due diligence, let’s go through what they represent.

Let’s start with option (A). In option (A), the only difference between both sides of our equation is we’ve rearranged our expression. We’ve swapped negative four and three. And there’s a few different ways we could arrive at this. For example, we could use our order of operations and the fact that we know when you add two numbers together, you can add them in either order. It won’t change the result. This would give us that these two sides of the equation are equal. However, this does not use the distributive property. Therefore, option (A) does not use the distributive property.

We can say something very similar about option (B). The only difference between both sides of the equation is we’re swapping the order of the terms. And once again, this does not use the distributive property.

In option (C), the only difference between our two sides of the equation is on the left-hand side we’re adding zero. And we know that these are equal because adding zero to a number doesn’t change its value. However, this does not use the distributive property.

Finally, let’s look at option (D). On the left-hand side of the expression in option (D), we have negative four multiplied by 𝑥 plus three. And we can see we’re indeed multiplying the sum of two values. So we could do this by using the distributive property of multiplication over addition. We multiply each of the terms inside of our parentheses by negative four and then add the result together. We get negative four 𝑥 plus negative four multiplied by three. And if we simplify this expression, we’ll see that we get a negative four 𝑥 minus 12. And this is exactly what is shown in option (D). Therefore, option (D) correctly demonstrates the distributive property of multiplication over addition.

And this gives us our final answer. Of the four options, only option (D) demonstrates the distributive property.