Answer
$\dfrac{4x^3-15x^2}{4x^2-20x+25}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\dfrac{(2x-5)\cdot3x^2-x^3\cdot2}{(2x-5)^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{(2x\cdot3x^2-5\cdot3x^2)-x^3\cdot2}{(2x-5)^2}
\\\\=
\dfrac{(6x^3-15x^2)-2x^3}{(2x-5)^2}
.\end{array}
Removing the grouping symbols and then combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{6x^3-15x^2-2x^3}{(2x-5)^2}
\\\\=
\dfrac{4x^3-15x^2}{(2x-5)^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{4x^3-15x^2}{(2x)^2-2(2x)(5)+(5)^2}
\\\\=
\dfrac{4x^3-15x^2}{4x^2-20x+25}
.\end{array}
