Answer: The required expanded form is 6x-9.
Step-by-step explanation: We are given to expand the following expression :
\(E=\dfrac{3}{8}(16x-24)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that, for any real numbers a, b and c, we have
\(a(b+c)=ab+ac.\)
So, from expression (i), we get
\(E\\\\\\=\dfrac{3}{8}(16x-24)\\\\\\=\dfrac{3}{8}\times16x-\dfrac{3}{8}\times24\\\\=6x-9.\)
Thus, the required expanded form is 6x-9.
