Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x ?
Simplify −4(7b+3)+24b−8
Simplify 2(3v+9)−14−6(−5v−4)
−15+45(15e−10)−10e
Factor 48y+36z using the GCF
Simple answers pls
The correct answer that applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x is:
23 − 18x − 45 + 11x
What about the second one?
The correct answer that applies the Distributive Property of Multiplication Over Addition correctly for simplifying 2(3v+9)−14−6(−5v−4) is:
6v + 18 - 14 + 30v + 24
Simplify −4(7b+3)+24b−8 I meant this one
To simplify the expression −4(7b+3)+24b−8 using the Distributive Property of Multiplication Over Addition, we can apply the following steps:
1. Distribute the -4 to the terms inside the parentheses:
−4(7b+3) = -4*7b + (-4)*3 = -28b - 12
2. Rewrite the expression with the simplified terms:
-28b - 12 + 24b - 8
3. Combine like terms:
-28b + 24b - 12 - 8 = -4b - 20
Therefore, the simplified expression is -4b - 20.
To apply the Distributive Property of Multiplication Over Addition correctly, we need to distribute the multiplication to every term inside the parentheses. Let's go through each answer choice to see if it applies the distributive property correctly:
1. Simplify −4(7b+3)+24b−8:
To apply the distributive property, we multiply -4 by both terms inside the parentheses:
-4 * 7b = -28b
-4 * 3 = -12
Therefore, the expression can be simplified as follows: -28b - 12 + 24b - 8.
2. Simplify 2(3v+9)−14−6(−5v−4):
To apply the distributive property, we multiply 2 by both terms inside the first parentheses, and we multiply -6 by both terms inside the second parentheses:
2 * 3v = 6v
2 * 9 = 18
-6 * -5v = 30v
-6 * -4 = 24
Therefore, the expression can be simplified as follows: 6v + 18 - 14 + 30v + 24.
3. Simplify −15+45(15e−10)−10e:
To apply the distributive property, we multiply 45 by both terms inside the parentheses:
45 * 15e = 675e
45 * -10 = -450
Therefore, the expression can be simplified as follows: -15 + 675e - 450 - 10e.
4. Factor 48y+36z using the GCF:
The GCD (Greatest Common Divisor) or GCF (Greatest Common Factor) of 48 and 36 is 12. We can factor out 12 from both terms:
12 * 4y = 48y
12 * 3z = 36z
Therefore, the expression can be factored as follows: 12(4y + 3z).
After analyzing each answer choice, the correct application of the Distributive Property of Multiplication Over Addition is in the second option:
2(3v+9)−14−6(−5v−4),
which simplifies to 6v + 18 - 14 + 30v + 24.