Rewrite each expression using the distributive property and simpl...

Question

Rewrite each expression using the distributive property and simplify, if possible. See Example 7.x + x

Accepted Answer

Hello, everyone. We are asked to apply the distributive property to rewrite the given expression and simplify. If necessary, we are given seven W plus seven, W our answer choices are a seven, W multiplied by the parenthesis. Seven plus seven equals 98. W bw multiplied by the parentheses. Seven plus seven equals 14 W C seven W multiplied by the parentheses. One plus seven equals 56 W DW multiplied by the parentheses. One plus one equals two. W first recall the distributive property states, if we have a value outside of a parentheses, that has a sum in it. So a multiplied by the parentheses, B plus C, we would multiply each term within the parentheses by the value on the outside. So we'd have a B plus AC here, we're given something similar to the second half. We have seven W plus seven. W now there are a few different ways we can backtrack this to get parentheses. So my first way, I'm gonna look for something they both have in common. Well, they are the exact same terms. So it's possible that seven W itself would be what goes on the outside of the parentheses. And then to find what goes inside, I would divide each term by seven W and seven W divided by seven, W would be one plus seven, W divided by seven, W would be one. So we would have seven, W multiplied by the parentheses. One plus one. This is not in our answer choices. So this must not be how we want it to be rewritten. So let's come up with another combination. So seven W plus seven W, they both also have a seven. So let's pull that to the outside of the parentheses. And when I divide each term by seven, seven, W divided by seven would be W plus seven W divided by seven BW. So another option would be seven multiplied by the parentheses. W plus W again, that one's not in our answer choice either. So third option again, we have seven W plus seven W. The other thing they both have in common for terms is a W. So let's factor A W or divide a W out of each term. So seven W divided by W is seven plus seven, W divided by W is seven, giving us W multiplied by the parentheses, seven plus seven, that one is in our answer choices. So this is the rewriting that we are going to stick with. Now to find out what this equals. When we simplify it, we could either go back to our original expression of seven W plus seven W and combine like terms to get 14 W or we can take our version with parentheses, W multiplied by the parentheses. Seven plus seven. Combine like terms within the parentheses giving us W multiplied by 14 and then rewrite W multiplied by 14 as 14. W either way when simplified it comes out to 14 W and this is answer choice BW multiplied by the parentheses. Seven plus seven equals 14. W have a nice day.

Rewrite each expression using the distributive property and simplify, if possible. See Example 7.x + x

Key Concepts

Distributive Property

Combining Like Terms

Simplification of Expressions

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