Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x?(1 point)Responses

Answer 1

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

Answer 2

Simplify −4(7b+3)+24b−8

Answer 3

-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

Answer 4

Simplify 2(3v+9)−14−6(−5v−4) .(1 point)

Answer 5

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.

Answer 6

−15+4/5(15e−10)−10e.(1 point)Responses

Answer 7

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.

Answer 8

Factor 48y+36z using the GCF.

Answer 9

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).