Which of the following answers applies the distributive property of multiplication over addition correctly simplifying 23 - 9 (2x + 5) + 11x?

23 - 9 (2x + 5) + 11x = 23 - 18x - 45 + 11x

Simplify -4 (7b + 3) + 24b - 8.

-4(7b + 3) + 24b - 8

= -28b - 12 + 24b - 8

= -4b - 20

simplify 2 (3v + 9) -- 14 - 6 (-5v -4)

2(3v + 9) - (-14) - 6(-5v - 4)

= 6v + 18 + 14 + 30v + 24

= 36v + 56

-15 + 4/5 (15e - 10) - 10e

-15 + (4/5)(15e - 10) - 10e

= -15 + (4/5)(15e) - (4/5)(10) - 10e

= -15 + (12e) - 8 - 10e

Now, let's combine like terms:

= (12e - 10e) - 15 - 8

= 2e - 23

factor 48y + 36z using the GCF.

To factor out the greatest common factor (GCF) of 48y and 36z, we need to find the largest number that divides evenly into both terms.

The prime factorization of 48 is 2^4 * 3, and the prime factorization of 36 is 2^2 * 3^2.

The GCF of 48y and 36z is 12, since it is the highest power of 2 and 3 that can be divided evenly into both terms.

Therefore, we can factor out 12 from both terms:

48y + 36z = 12 * (4y + 3z)

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