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

You need to know the distributive property

\( a(b-c) = ab - ac\)

Now take a look at the work that the student did

Pay extra attention to the signs and the plus or minuses in the expression

We have -6 and we're distributing that inside

This is also an important concept that you should know:
positive number * positive number = positive number
negative number * negative number = positive number
positive number * negative number = negative number
negative number * positive number = negative number

Answer 2

re-writing the work that the student did for clarity

\(−6 \left(4x − \dfrac{2}{13}\right) \)

\(−6(4x) + 6\left( −\dfrac{2}{13}\right) \)

\( −24x − \dfrac{12}{13}\)

Answer 3

So let me add colors for you

\(\large \color{orange}{a}(b\color{red}{−}c) = \color{orange}{a}b \color{red}{−} \color{orange}{a}c\)

So in our question, the 'a' is -6

But do you see how that minus sign stays? You can later simplify depending on the value of 'c' using the properties I mentioned above

Answer 4

So did the student make a mistake?

And if so, where?