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.
