Sure, let's simplify the mathematical expression [tex]\(\left(\frac{48}{8} e f - 6 g\right)^2\)[/tex] step-by-step.
### Step 1: Evaluate the fraction
First, simplify the fraction [tex]\(\frac{48}{8}\)[/tex]:
[tex]\[
\frac{48}{8} = 6
\][/tex]
### Step 2: Substitute the simplified fraction back into the expression
Now replace [tex]\(\frac{48}{8}\)[/tex] with 6:
[tex]\[
(6ef - 6g)^2
\][/tex]
### Step 3: Factor out the common term from the expression inside the parentheses
Notice that both terms [tex]\(6ef\)[/tex] and [tex]\(6g\)[/tex] have a common factor of 6:
[tex]\[
6(ef - g)
\][/tex]
### Step 4: Express the entire expression in factored form
The expression [tex]\((6(ef - g))^2\)[/tex] can be simplified further by applying the exponent:
[tex]\[
(6(ef - g))^2 = 6^2 \cdot (ef - g)^2
\][/tex]
### Step 5: Evaluate the exponent for the constant term
Calculate [tex]\(6^2\)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
### Step 6: Combine the results
Therefore, the expression simplifies to:
[tex]\[
36(ef - g)^2
\][/tex]
So, the final simplified form of the given expression [tex]\(\left(\frac{48}{8} e f - 6 g\right)^2\)[/tex] is:
[tex]\[
36(ef - g)^2
\][/tex]
