In Exercises 117–130, simplify each algebraic expression. 5(3y-2)...

Question

In Exercises 117–130, simplify each algebraic expression. 5(3y-2)-(7y+2)

Accepted Answer

Welcome back. I am so glad you're here. We are asked to simplify the expression eight multiplied by open parentheses. Seven A minus six closed parentheses minus open parentheses. 15 A plus 14 closed parentheses. And we are given the answer choices. Answer choice, A 71 A plus 62 answer choice B 41 A minus 62 answer choice C negative 71 A minus 62 answer choice D negative 41 A plus 62. And in order to simplify the expression, we need to recall from previous lessons. The order of operations, we will begin with parentheses, followed by exponents, followed by multiplication and division from left to right, followed by addition and subtraction from left to right. That's our acronym. So we start off with parentheses and we have two sets of parentheses. We can begin with the one on the left. The one on the left is seven A minus six. And we want to do the operation inside of the parentheses. However, the operation here is subtraction and we can only subtract like terms. Seven A and six are not like terms. So how do we deal with this parentheses? Well, next, we look in front of the parentheses and see if there's any number squished up against them that needs to be distributed. And the number here that's in front of the parentheses is a positive eight. So this eight needs to be distributed to both the seven A and the negative six. So we can do that. Eight multiplied by seven A is 56 A and eight multiplied by -6 is -48. So we put -48. Now we can deal with the other set of parentheses here. The second set of parentheses is 15 A plus 14. The operation in there is addition, but again, they're not like terms. So we look in front and we see no number, we just see a negative. Well, that negative, it's really a negative one. That negative one needs to be distributed to both the 15 A and the 14. So negative one multiplied by 15 A equals a negative 15. A, A -1 multiplied by a positive 14 equals a -14. So now our expression is 56 A minus 48 minus 15 A minus 14. There are no more parentheses. There are no exponents, there's no multiplication or division. We only need to add and subtract like terms. So the like terms here are, we can start with the A's, we have 56 A minus 15 A that will leave us with 41 A and now we have the constant terms, we have negative 48 a negative 14. Well, negative 48 minus 14 equals a negative 62. So here is our simplified expression. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

In Exercises 117–130, simplify each algebraic expression. 5(3y-2)-(7y+2)

Key Concepts

Distributive Property

Combining Like Terms

Negative Sign Distribution

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