In Exercises 117–130, simplify each algebraic expression. 18x²+4-...

Question

In Exercises 117–130, simplify each algebraic expression. 18x²+4-[6(x²-2)+5]

Accepted Answer

Hello, everyone. We are going to simplify the expression 21 X cubed plus nine minus open square bracket. Two multiplied by open parentheses. X cubed minus 11 closed parentheses plus 18 closed square bracket. Our answer choices are a 23 x cubed - B 19 x cubed plus C- 23 x cubed plus D 19 x cubed -13. I'm going to rewrite my expression 21 X cubed plus nine minus open square bracket. Two multiplied by open parentheses. X cubed minus 11 closed parentheses plus 18 closed square bracket. I recall that I want to simplify this as much as I can. I'm gonna start from the innermost set of grouping symbols and work outward. So my innermost set of grouping symbols is X cubed - and there's a two right outside of it, meaning the two needs to be distributed into the parentheses. X cubed -11. So I'm going to rewrite the rest of my expression 21 X cubed plus nine minus open square bracket. And then I'm distributing the two into the parentheses. Two multiplied by X cubed is 2 x cubed two multiplied by negative 11 is minus or negative 22 plus 18, which did not change closed square bracket from here. I'm going to simplify what I can within my square bracket. So again, rewriting the rest of the expression 21 X cubed plus nine minus open square bracket and inside the bracket, there is no like term for the two X cubed. So I'm rewriting that and I'm going to combine negative 22 positive 18 to be a negative four closed square bracket. Next, I wanna see what I can do to get rid of these square brackets right out front of the square bracket. I have a minus sign. So I'm gonna distribute that into the square bracket as if it is a negative one. So 21 x cubed plus nine still has not changed. And I'm distributing this minus sign in as if it's a -1. So negative one multiplied by two X cubed is negative two X cubed, negative one multiplied by negative four is plus four or positive four. So now I have 21 X cubed plus nine minus two X cubed plus four. I've gotten rid of all of the grouping symbols. So now we're gonna combine our like terms. Recall that like terms again are the same variable with the same exponent. So X cubed is the first ones I'm going to combine. So I'm gonna combine 21 X cubed and negative two X cubed 21 plus negative two gives me 19. So 19 x cubed is my first term and then I'm gonna combine positive nine and positive four which will be positive 13. So plus 13 and now that I have no more like terms, this is my solution. 19 X cubed plus 13 which is answer choice B have a nice day.

In Exercises 117–130, simplify each algebraic expression. 18x²+4-[6(x²-2)+5]

Key Concepts

Distributive Property

Combining Like Terms

Order of Operations

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