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)
The expression that simplifies to the same expression as 4x^2−3x^2+5x−24 is (x+8)(x-3).
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
(9x^2+17x+13)−(2x^2+12x+11) simplifies to 7x^2+5x+2.
Multiply the polynomials (3x−1)(2x+4) .
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.
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
The response that shows that polynomials form a closed system under multiplication is "4x^3 * 5".
Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2.
22r-13
19r+(3r-2)-11
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.
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
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.
Are you sure? Where did 2x^2 go?
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.