Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x ?(1 point
23 - 9(2x + 5) + 11x can be simplified by applying the Distributive Property of Multiplication Over Addition.
The correct answer would be:
23 - 18x - 45 + 11x.
Simplify −4(7b+3)+24b−8 .(1 point)
To simplify -4(7b + 3) + 24b - 8, we can apply the Distributive Property of Multiplication Over Addition.
Multiply -4 by each term in the parentheses:
-4 * 7b = -28b
-4 * 3 = -12
The expression now becomes: -28b - 12 + 24b - 8.
Next, combine the like terms:
-28b + 24b = -4b
-12 - 8 = -20
The simplified expression is -4b - 20.
Simplify 2(3v+9)−14−6(−5v−4).(1 point)
To simplify 2(3v + 9) - 14 - 6(-5v - 4), we can apply the Distributive Property of Multiplication Over Addition.
Multiply 2 by each term in the first parentheses:
2 * 3v = 6v
2 * 9 = 18
The expression now becomes: 6v + 18 - 14 - 6(-5v - 4).
Multiply -6 by each term in the second parentheses:
-6 * -5v = 30v
-6 * -4 = 24
The expression now becomes: 6v + 18 - 14 - 30v - 24.
Combine the like terms:
6v - 30v = -24v
18 - 14 - 24 = -20
The simplified expression is -24v - 20.
−15+4/5(15e−10)−10e
To simplify -15 + 4/5(15e - 10) - 10e, we can apply the Distributive Property of Multiplication Over Addition.
Multiply 4/5 by each term inside the parentheses:
4/5 * 15e = 12e
4/5 * -10 = -8
The expression now becomes: -15 + 12e - 8 - 10e.
Combine like terms:
12e - 10e = 2e
-15 - 8 = -23
The simplified expression is 2e - 23.
Factor 48y+36z using the GCF
To factor 48y + 36z using the GCF (Greatest Common Factor), we need to find the largest number or variable that can divide both terms.
The GCF of 48y and 36z is 12 since both terms are divisible by 12.
So, we can factor out 12 from both terms:
48y can be written as 12 * 4y, and
36z can be written as 12 * 3z.
So, the expression 48y + 36z can be factored as 12(4y + 3z).
To apply the Distributive Property of Multiplication Over Addition correctly for simplifying the expression 23−9(2x+5)+11x, we need to distribute the -9 to both terms inside the parentheses, which are 2x and 5.
Using the Distributive Property, we multiply -9 by 2x and -9 by 5. The expression becomes:
23 - 18x - 45 + 11x
Now, we combine like terms. -18x and 11x are like terms, so they can be combined:
-18x + 11x = -7x
The simplified expression is:
23 - 45 - 7x
Now, we combine the numerical terms:
23 - 45 = -22
The final simplified expression is:
-22 - 7x
So, the correct application of the Distributive Property of Multiplication Over Addition for simplifying the expression 23−9(2x+5)+11x is:
-22 - 7x.