Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x?(1 point)Responses
23−9(2x+5)+11x
Distributive Property: a(b+c) = ab + ac
Using the Distributive Property, first distribute -9 to 2x and 5:
23 − 9(2x) − 9(5) + 11x
Simplifying:
23 - 18x - 45 + 11x
Simplify −4(7b+3)+24b−8
-4(7b+3)+24b-8
Using the distributive property, distribute -4 to both terms inside the parentheses:
-4(7b) - 4(3) + 24b - 8
Simplifying:
-28b - 12 + 24b - 8
Combining like terms:
(-28b + 24b) + (-12 - 8)
Simplifying further:
-4b - 20
Simplify 2(3v+9)−14−6(−5v−4) .(1 point)
To simplify the expression 2(3v+9)−14−6(−5v−4), we apply the distributive property:
2(3v+9)−14−6(−5v−4)
= 6v + 18 - 14 + 30v + 24
Combine like terms:
= 36v + 28
So, the simplified expression is 36v + 28.
−15+4/5(15e−10)−10e.(1 point)Responses
To simplify the expression -15 + 4/5(15e - 10) - 10e, we apply the distributive property:
= -15 + (4/5)(15e - 10) - 10e
= -15 + (4/5)(15e) - (4/5)(10) - 10e
= -15 + (4/5)(15e) - 8 - 10e
Next, we distribute (4/5) to both terms inside the parentheses:
= -15 + (4/5)(15e) - 8 - 10e
= -15 + (4/5)(15e) - 8 - 10e
= -15 + (60/5)e - 8 - 10e
Now we simplify:
= -15 + 12e - 8 - 10e
= 2e - 23
So, the simplified expression is 2e - 23.
Factor 48y+36z using the GCF.
To factor out the greatest common factor (GCF) from the expression 48y + 36z, we need to identify the highest common factor of the coefficients 48 and 36 (which is 12) and the common variable 'y' and 'z'.
The GCF of 48 and 36 is 12.
The GCF of 'y' and 'z' is 1 since they have no other common factors.
Thus, the GCF of 48y and 36z is 12yz.
Now, we can factor out the GCF:
48y + 36z = 12yz(4y + 3)
So, by factoring out the GCF, the expression 48y + 36z becomes 12yz(4y + 3).
To apply the Distributive Property of Multiplication Over Addition correctly, you need to multiply each term inside the parentheses by the number outside the parentheses. In this case, you need to multiply -9 by both 2x and 5.
Let's simplify the expression step by step:
23 - 9(2x + 5) + 11x
First, distribute -9 to both terms inside the parentheses:
23 - (9 * 2x) - (9 * 5) + 11x
Simplifying further:
23 - 18x - 45 + 11x
Now, combine like terms:
(23 - 45) + (-18x + 11x)
-22 + (-7x)
Therefore, the correct answer applying the Distributive Property of Multiplication Over Addition is -22 - 7x.