Students were asked to use the distributive property to write an equivalent expression for the expression 8−3(2+4k)

Question

.

Their work is shown below. Identify the student with the correct work. For the answers that are incorrect, explain where the students made mistakes.

Student 1

8−3(2+4k)

8−6+12k

2+12k



Student 2:

8−3(2+4k)

8−6−12k

2−12k



Student 3:

8−3(2+4k)

8−6−12k
2−12k
−10k

Answer 1

The student with the correct work is Student 1.

Student 2 made a mistake by subtracting 6 instead of adding 6 in the first step. The correct step should be:

8 - 3(2 + 4k)
8 - 3(2) - 3(4k)
8 - 6 - 12k

Student 3 also made a mistake in the second step by subtracting 6 instead of adding 6. The correct step should be:

8 - 3(2 + 4k)
8 - 3(2) - 3(4k)
8 - 6 - 12k
2 - 12k

Thus, Student 1 is the only one who correctly applied the distributive property.