Question
Which of the following simplifies to the same expression as 4x^2−3x^2+5x−24
4x(x-6)
(x+8)(x-3)
(x+6)(x-4)
2(x-12)
4x(x-6)
(x+8)(x-3)
(x+6)(x-4)
2(x-12)
Answers
GPT 3.5
The expression that simplifies to the same expression as 4x^2−3x^2+5x−24 is (x+8)(x-3).
Pls help
Which of the following correctly simplifies (9x^2+17x+13)−(2x^2+12x+11)?
9x2+17x+13−2x2−12x−11 9 x squared plus 17 x plus 13 minus 2 x squared minus 12 x minus 11 7x2+5x+2 7 x squared plus 5 x plus 2 12x2+2 12 x squared plus 2 7x2+29x+24
9x2+17x+13−2x2−12x−11 9 x squared plus 17 x plus 13 minus 2 x squared minus 12 x minus 11 7x2+5x+2 7 x squared plus 5 x plus 2 12x2+2 12 x squared plus 2 7x2+29x+24
GPT 3.5
(9x^2+17x+13)−(2x^2+12x+11) simplifies to 7x^2+5x+2.
Pls help
Multiply the polynomials (3x−1)(2x+4) .
GPT 3.5
To multiply the polynomials (3x - 1)(2x + 4), you need to use the distributive property.
(3x - 1)(2x + 4) can be expanded as follows:
= 3x(2x) + 3x(4) - 1(2x) - 1(4)
= 6x^2 + 12x - 2x - 4
= 6x^2 + 10x - 4
Therefore, (3x - 1)(2x + 4) simplifies to 6x^2 + 10x - 4.
(3x - 1)(2x + 4) can be expanded as follows:
= 3x(2x) + 3x(4) - 1(2x) - 1(4)
= 6x^2 + 12x - 2x - 4
= 6x^2 + 10x - 4
Therefore, (3x - 1)(2x + 4) simplifies to 6x^2 + 10x - 4.
Pls help
Which of the following responses shows that polynomials form a closed system under multiplication?
(x)(1/2x)
3x^2/4-1
4x^3*5
6*-3
(x)(1/2x)
3x^2/4-1
4x^3*5
6*-3
GPT 3.5
The response that shows that polynomials form a closed system under multiplication is "4x^3 * 5".
Pls help
Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2.
22r-13
19r+(3r-2)-11
22r-13
19r+(3r-2)-11
GPT 3.5
Expression 1: 22r - 13
Expression 2: 19r + (3r - 2) - 11
The associative property states that you can change the grouping of terms when adding or subtracting without changing the result.
Let's apply the associative property to Expression 2 by rearranging the grouping of terms:
19r + (3r - 2) - 11
We can first group the terms within the parentheses:
(19r + 3r - 2) - 11
Now let's combine like terms within the parentheses:
(22r - 2) - 11
Finally, let's combine the two terms outside of the parentheses:
22r - 2 - 11
Simplifying further:
22r - 13
We can see that Expression 2, after applying the associative property, simplifies to Expression 1. Therefore, Expression 1 is equivalent to Expression 2.
Expression 2: 19r + (3r - 2) - 11
The associative property states that you can change the grouping of terms when adding or subtracting without changing the result.
Let's apply the associative property to Expression 2 by rearranging the grouping of terms:
19r + (3r - 2) - 11
We can first group the terms within the parentheses:
(19r + 3r - 2) - 11
Now let's combine like terms within the parentheses:
(22r - 2) - 11
Finally, let's combine the two terms outside of the parentheses:
22r - 2 - 11
Simplifying further:
22r - 13
We can see that Expression 2, after applying the associative property, simplifies to Expression 1. Therefore, Expression 1 is equivalent to Expression 2.
Pls help
Use the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work.
Expression 1: (x−5)(x+3)
Expression 2: 2x^2−x^2−2x−20+5
Expression 1: (x−5)(x+3)
Expression 2: 2x^2−x^2−2x−20+5
GPT 3.5
Expression 1: (x - 5)(x + 3)
Expression 2: 2x^2 - x^2 - 2x - 20 + 5
To prove that these expressions are equivalent, we need to show that the result is the same when we multiply them out.
Using the distributive property, we can expand Expression 1:
(x - 5)(x + 3) = x(x) + x(3) - 5(x) - 5(3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15
Simplifying, we have x^2 - 2x - 15.
Comparing this to Expression 2, we can see that both expressions have the same resulting algebraic expression: x^2 - 2x - 15.
Therefore, we have demonstrated that Expression 1 is equivalent to Expression 2, as they both simplify to the same algebraic expression x^2 - 2x - 15.
Expression 2: 2x^2 - x^2 - 2x - 20 + 5
To prove that these expressions are equivalent, we need to show that the result is the same when we multiply them out.
Using the distributive property, we can expand Expression 1:
(x - 5)(x + 3) = x(x) + x(3) - 5(x) - 5(3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15
Simplifying, we have x^2 - 2x - 15.
Comparing this to Expression 2, we can see that both expressions have the same resulting algebraic expression: x^2 - 2x - 15.
Therefore, we have demonstrated that Expression 1 is equivalent to Expression 2, as they both simplify to the same algebraic expression x^2 - 2x - 15.
Pls help
Are you sure? Where did 2x^2 go?
GPT 3.5
You are right, I apologize for the error. Let's correct the explanation.
Expression 1: (x - 5)(x + 3)
Expression 2: 2x^2 - x^2 - 2x - 20 + 5
Using the distributive property, we can expand Expression 1:
(x - 5)(x + 3) = x(x) + x(3) - 5(x) - 5(3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15
So the expanded form of Expression 1 is x^2 - 2x - 15.
Comparing this to Expression 2, we can see that Expression 2 is also equal to x^2 - 2x - 15.
Therefore, we have demonstrated that Expression 1 is equivalent to Expression 2, as they both simplify to the same algebraic expression x^2 - 2x - 15.
Expression 1: (x - 5)(x + 3)
Expression 2: 2x^2 - x^2 - 2x - 20 + 5
Using the distributive property, we can expand Expression 1:
(x - 5)(x + 3) = x(x) + x(3) - 5(x) - 5(3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15
So the expanded form of Expression 1 is x^2 - 2x - 15.
Comparing this to Expression 2, we can see that Expression 2 is also equal to x^2 - 2x - 15.
Therefore, we have demonstrated that Expression 1 is equivalent to Expression 2, as they both simplify to the same algebraic expression x^2 - 2x - 15.