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## Distributive property with variables

# Distributive property over subtraction

CCSS.Math:

## Video transcript

Rewrite the expression five
times 9 minus 4-- that's in parentheses-- using the
distributive law of multiplication over
subtraction. Then simplify. So let me just rewrite it. This is going to be 5 times
9 minus 4, just like that. Now, if we want to use the
distributive property, well, you don't have to. You could just evaluate
9 minus 4 and then multiply that times 5. But if you want to use the
distributive property, you distribute the 5. You multiply the 5 times the 9
and the 4, so you end up with 5 times 9 minus 5 times 4. Notice, we distributed the 5. We multiplied it times
both the 9 and the 4. In the first distributive
property video, we gave you an idea of why you have to
distribute the 5, why it makes sense, why you don't just
multiply it by the 9. And we're going to verify that
it gives us the same answer as if we just evaluated the 9 minus
4 first. But anyway, what are these things? So 5 times 9, that is 45. So we have 45 minus--
what's 5 times 4? Well, that's 20. 45 minus 20, and that is equal
to 25, so this is using the distributive property
right here. If we didn't want to use the
distributive property, if we just wanted to evaluate what's
in the parentheses first, we would have gotten-- let's go in
this direction-- 5 times-- what's 9 minus 4? 9 minus 4 is 5. Let me do that in a
different color. 5 times 9 minus 4. So it's 5 times 5. 5 times 5 is just 25,
so we get the same answer either way. This is using the distributive
law of multiplication over subtraction, usually just
referred to as the distributive property. This is evaluating the inside
of the parentheses first and then multiplying by 5.