Question

A student expanded an expression, as shown. Is the student's work correct? Explain why or why not.


−6 ( 4x −
2
13
)

−6(4x) + 6 ( −
2
13
)

−24x −
12
13

Answer 1

The work is not correct. When you distribute −6 you must multiply it by each term and keep the signs:

−6(4x − 2/13) = (−6)(4x) + (−6)(−2/13) = −24x + 12/13.

The student’s error was in handling the second product: (−6)(−2/13) = +12/13, not −12/13. (Check: put x = 0: original gives −6(−2/13) = 12/13, but the student’s result gives −12/13, so it’s wrong.)