Question

Tell how you can use the Distributive Property to write 12m + 8m in simplest form. Use the word "coefficient" in your explanation.

A) 12m + 8m = 20m, where 20 is the coefficient.
B) 12m + 8m = 20m, where 12 and 8 are coefficients.
C) 12m + 8m = 12m + 8m, coefficients don't change.
D) 12m + 8m = 96m, where 96 is the coefficient.

Answer 1

To simplify 12m + 8m, we add the coefficients 12 and 8 to get 20, thus the simplified expression is 20m, where 20 is the coefficient. The correct answer is A) 12m + 8m = 20m, where 20 is the coefficient.

Step-by-step explanation:

To use the Distributive Property to write 12m + 8m in its simplest form, we recognize that m is a common factor to both terms. In algebra, the numbers in front of the variable, which are 12 and 8 in this case, are called coefficients. Instead of distributing, in this particular instance, we are actually combining like terms because both terms have the same variable m. Therefore, we add the coefficients together:

• 12m + 8m = (12 + 8)m
• 12m + 8m = 20m

In this expression, 20 is the new coefficient for the variable m after we combined like terms.

Thus, the correct answer is A) 12m + 8m = 20m, where 20 is the coefficient.