<s>[INST] pre algebraic factoring with polynomials I really need help solving this particular problem. 
$$\frac14x^2y(x-1)^3-\frac54xy(x-1)^2$$
I need help factoring this. It seems like I need to get rid of the fraction but I really just need a little boost.
 [/INST] The given equation is
$$\dfrac{1}{4}x^2y(x - 1)^3 - \dfrac{5}{4}xy(x - 1)^2$$
Since the GCF (greatest common factor) is $\frac{1}{4}xy(x - 1)^2$, write the expression as
$$\begin{aligned}
\underbrace{\dfrac{1}{4}xy(x - 1)^2 \cdot x(x - 1)}_{\frac{1}{4}x^2y(x - 1)^3} - \underbrace{\dfrac{1}{4}xy(x - 1)^2 \cdot 5}_{\frac{5}{4}xy(x - 1)^2}&= \underbrace{\dfrac{1}{4}xy(x - 1)^2}_{\text{GCF}}\left(x(x - 1) - 5 \right)\\
&= \dfrac{1}{4}xy(x - 1)^2(x^2 - x - 5)
\end{aligned}$$
So the answer is
$$\dfrac{1}{4}xy(x - 1)^2(x^2 - x - 5)$$
Explanations for each step I have shown for your problem


*

*Extract the common factor out from each term you see, which is $\frac{1}{4}xy(x - 1)^2$ (Noticed that both terms have common terms $\frac{1}{4}$, $x$, $y$ and $(x - 1)^2$).  This is called the GCF.  Underneath each factored term, you see the original terms in the original equation.

*Factor out that term, leaving the uncommon factors (namely $x(x - 1)$ and $-5$) in the parentheses. (Multiple each term in the parentheses by $\frac{1}{4}xy(x - 1)^2$.  You should get the same answer.)

*Simplify the expression in the parentheses.

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