Question

I need help with this problem Evaluate each expression given the variable replacement

Answer 1

Given the expression:

$\frac{20ab}{\mleft(a-b\mright)^2}$

1. You need to substitute these values given in the exercise into the expression:

$\begin{gathered} a=4 \\ b=-2 \end{gathered}$

Then:

$=\frac{20(4)(-2)}{(4-(-2))^2}$

2. According to the Sign Rules for Multiplication:

$\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}$

Knowing this, you can solve the multiplication in the numerator and simplify the denominator:

$=\frac{-160}{(4+2)^2}$$=\frac{-160}{(6)^2}$

You know that:

$6^2=6\cdot6=36$

Then:

$=\frac{-160}{36}$

3. According to the Sign Rules for Division:

$\begin{gathered} \frac{-}{-}=+ \\ \\ \frac{+}{+}=+ \\ \\ \frac{-}{+}=- \\ \\ \frac{+}{-}=- \end{gathered}$

Therefore, since the numerator is negative and the denominator is positive, the fraction is negative:

$=-\frac{160}{36}$

4. You can reduce the fraction by dividing the numerator and the denominator by 4:

$\begin{gathered} =-\frac{160\div4}{36\div4} \\ \\ =-\frac{40}{9} \end{gathered}$

Hence, the answer is:

$=-\frac{40}{9}$