Students were asked to use the distributive property to write an equivalent expression for the expression 8−3(2+4k)
.
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
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.
To use the distributive property, we need to multiply -3 by each term inside the parentheses. Let's go through each student's work and identify the correct one:
Student 1:
8 − 3(2 + 4k)
8 − 6 + 12k
2 + 12k
Student 1 is correct. They correctly distributed -3 to both terms inside the parentheses.
Student 2:
8 − 3(2 + 4k)
8 − 6 - 12k
2 - 12k
Student 2 is incorrect. They incorrectly distributed -3 as -12k instead of 12k.
Student 3:
8 − 3(2 + 4k)
8 − 6 - 12k
2 - 12k
-10k
Student 3 is incorrect. They made the same mistake as Student 2 by incorrectly distributing -3 as -12k instead of 12k, and they made an additional mistake by simplifying it to -10k, which is not correct.
Therefore, Student 1 has the correct work with the equivalent expression of 2 + 12k.