Which expression is equivalent to −3x−5
?
−1+3x−(2x+6)
(−4x−6)+(2+5x)
−1+(x−4x)+6
(x−7)+(2−4x)
None of the given expressions are equivalent to −3x−5.
are you sure
Apologies for the confusion. You are right. The expression that is equivalent to −3x−5 is (−4x−6)+(2+5x).
According to the Distributive Property, which expression is equivalent to 4x^3+8x^2+12x
1 point)
Responses
4x(4x+5x)
(2x^2+4)(2x−3)
(2x^2+4)(2x^2+3)
4x(x^2+2x+3)
According to the Distributive Property, the expression that is equivalent to 4x^3+8x^2+12x is 4x(x^2+2x+3).
Which of the following simplifies to the same expression as 4x^2−3x^2+5x−24?(1 point)
Responses
4x(x−6)
2(x−12)
(x+8)(x−3)
(x+6)(x−4)
The expression that simplifies to the same expression as 4x^2−3x^2+5x−24 is (x+6)(x-4).
Add the polynomial expressions 5z−2z^2−4z+5
and 6z^2+3−7z
To add the polynomial expressions, we add the like terms together:
(5z - 2z^2 - 4z + 5) + (6z^2 + 3 - 7z)
First, let's combine the like terms with z^2: -2z^2 + 6z^2 = 4z^2
Next, we combine the like terms with z: 5z - 4z - 7z = -6z
Finally, we combine the constant terms: 5 + 3 = 8
Putting it all together, the sum of the polynomial expressions is:
4z^2 - 6z + 8.
correctly simplify (9x^2+17x+13)−(2x^2+12x+11)
To simplify (9x^2 + 17x + 13) - (2x^2 + 12x + 11), we need to distribute the negative sign to each term inside the parentheses:
9x^2 + 17x + 13 - 2x^2 - 12x - 11
Next, we can combine like terms:
(9x^2 - 2x^2) + (17x - 12x) + (13 - 11)
This simplifies to:
7x^2 + 5x + 2
So, the simplified expression is 7x^2 + 5x + 2.
Multiply the polynomials (3x−1)(2x+4)
To multiply the polynomials (3x - 1)(2x + 4), we will use the distributive property.
First, we multiply 3x by each term in the second polynomial:
3x * 2x = 6x^2
3x * 4 = 12x
Next, we multiply -1 by each term in the second polynomial:
-1 * 2x = -2x
-1 * 4 = -4
Now, we can combine like terms:
(6x^2 + 12x) + (-2x - 4)
This simplifies to:
6x^2 + 12x - 2x - 4
Combining like terms again:
6x^2 + (12x - 2x) - 4
This further simplifies to:
6x^2 + 10x - 4
So, the product of the polynomials (3x - 1)(2x + 4) is 6x^2 + 10x - 4.
Which of the following responses shows that polynomials form a closed system under multiplication?(1 point)
Responses
4x3⋅5
3x2/4−1
6⋅−3
(x)(1/2 x)
The correct response that shows that polynomials form a closed system under multiplication is 4x^3 * 5. When we multiply two polynomials together, the resulting expression is still a polynomial, so the system is closed under multiplication.
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)
To expand this expression using the Distributive Property, we multiply each term in the first parentheses (x and -5) with each term in the second parentheses (x and 3):
(x * x) + (x * 3) + (-5 * x) + (-5 * 3)
After simplifying, we get:
x^2 + 3x - 5x - 15
Combining like terms, we have:
x^2 - 2x - 15
Expression 2: 2x^2 - x^2 - 2x - 20 + 5
To simplify this expression, we combine like terms:
(2x^2 - x^2) - 2x - 20 + 5
After simplifying, we get:
x^2 - 2x - 15
Explanation:
Both calculations simplify to x^2 - 2x - 15, demonstrating the equivalence between Expression 1 and Expression 2.
explain why the following operation is a closed system under subtraction.
(9x2+17x+13)−(2x2+12x+11)