Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x ?(1 point)
Simplify −4(7b+3)+24b−8 .(1 point)
To simplify the expression -4(7b+3) + 24b - 8, we use the Distributive Property of Multiplication over Addition/Subtraction.
Applying the Distributive Property, we have:
-4 * 7b + -4 * 3 + 24b - 8
Simplifying further, we get:
-28b - 12 + 24b - 8
Combining like terms, we get:
-4b - 20
So, the simplified expression is -4b - 20.
Simplify 2(3v+9)−14−6(−5v−4) .(1 point)
To simplify the expression 2(3v+9)−14−6(−5v−4), we use the Distributive Property of Multiplication over Addition/Subtraction.
We will simplify each term separately:
2(3v+9) simplifies to 6v + 18
-6(-5v-4) simplifies to 30v + 24
So, now the expression becomes:
6v + 18 - 14 + 30v + 24
Combining like terms, we get:
36v + 28
Therefore, the simplified expression is 36v + 28.
−15+45(15e−10)−10e .(1 point)
To simplify the expression -15 + 45(15e - 10) - 10e, we use the Distributive Property of Multiplication over Addition/Subtraction.
First, let's simplify the term 45(15e - 10):
45(15e - 10) simplifies to 675e - 450.
Now, the expression becomes:
-15 + 675e - 450 - 10e.
Combining like terms, we get:
665e - 465 - 10e.
Finally, combining like terms again, we get:
(665e - 10e) - 465.
Simplifying this, we get:
655e - 465.
Therefore, the simplified expression is 655e - 465.
−15+4/5(15e−10)−10e .(1 point)
To simplify the expression -15 + 4/5(15e - 10) - 10e, we use the Distributive Property of Multiplication over Addition/Subtraction.
First, let's simplify the term 4/5(15e - 10):
4/5 * 15e = (4/5) * 15e = 12e
4/5 * -10 = (4/5) * -10 = -8
Therefore, 4/5(15e - 10) simplifies to 12e - 8.
Now, the expression becomes:
-15 + 12e - 8 - 10e.
Combining like terms, we get:
12e - 10e - 15 - 8.
Further simplifying, we get:
12e - 10e - 23.
Finally, combining like terms again, we get:
(12e - 10e) - 23.
Simplifying this, we get:
2e - 23.
Therefore, the simplified expression is 2e - 23.
Factor 48y+36z using the GCF.
To factor 48y + 36z using the greatest common factor (GCF), we need to find the largest number that can divide both 48 and 36.
The GCF of 48 and 36 is 12, which can be found by finding the common factors of 48 and 36 (1, 2, 3, 4, 6, 12) and selecting the largest one.
Now, we can write the expression as the product of the GCF and a simplified expression:
48y + 36z = 12(4y + 3z)
So, the factored form of 48y + 36z using the GCF is 12(4y + 3z).
Simplify 5(7x−2)−14x+4 .(1 point)
To simplify the expression 5(7x - 2) - 14x + 4, we use the Distributive Property of Multiplication over Addition/Subtraction.
First, let's simplify the term 5(7x - 2):
5(7x) = 35x
5(-2) = -10
Therefore, 5(7x - 2) simplifies to 35x - 10.
Now, the expression becomes:
35x - 10 - 14x + 4.
Combining like terms, we get:
(35x - 14x) + (-10 + 4).
Further simplifying, we get:
21x - 6.
Therefore, the simplified expression is 21x - 6.
Simplify 17d−33+9(2d+6)−11 .
To simplify the expression 17d - 33 + 9(2d + 6) - 11, we use the Distributive Property of Multiplication over Addition/Subtraction.
First, let's simplify the term 9(2d + 6):
9(2d) = 18d
9(6) = 54
Therefore, 9(2d + 6) simplifies to 18d + 54.
Now, the expression becomes:
17d - 33 + 18d + 54 - 11.
Combining like terms, we get:
(17d + 18d) + (-33 + 54 - 11).
Further simplifying, we get:
35d + 10.
Therefore, the simplified expression is 35d + 10.
Simplify 6(3q−4)+18−12q−7(4q+5) .(1 point)
To simplify the expression 6(3q - 4) + 18 - 12q - 7(4q + 5), we use the Distributive Property of Multiplication over Addition/Subtraction.
First, let's simplify the term 6(3q - 4):
6(3q) = 18q
6(-4) = -24
Therefore, 6(3q - 4) simplifies to 18q - 24.
Next, let's simplify the term 7(4q + 5):
7(4q) = 28q
7(5) = 35
Therefore, 7(4q + 5) simplifies to 28q + 35.
Now, the expression becomes:
18q - 24 + 18 - 12q - (28q + 35).
Combining like terms, we get:
(18q - 12q - 28q) + (-24 + 18 - 35).
Further simplifying, we get:
-22q - 41.
Therefore, the simplified expression is -22q - 41.
The correct application of the Distributive Property of Multiplication Over Addition for simplifying 23−9(2x+5)+11x is:
23 - 9(2x) - 9(5) + 11x.