Answer
$\dfrac{13}{25x^2-20x+4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\dfrac{(4x+1)\cdot5-(5x-2)\cdot4}{(5x-2)^2}
,$ use the Distributive Property first. Then remove the grouping symbols and combine like terms. Finally, use special products to simplify the denominator.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{(4x\cdot5+1\cdot5)-(5x\cdot4-2\cdot4)}{(5x-2)^2}
\\\\=
\dfrac{(20x+5)-(20x-8)}{(5x-2)^2}
.\end{array}
Removing the grouping symbols and then combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{20x+5-20x+8}{(5x-2)^2}
\\\\=
\dfrac{13}{(5x-2)^2}
\\\\=
\dfrac{13}{(5x-2)^2}
.\end{array}
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{13}{(5x)^2-2(5x)(2)+(2)^2}
\\\\=
\dfrac{13}{25x^2-20x+4}
.\end{array}
