Hello. I need to factor this equation and I'm a bit stumped.
The equation is $\displaystyle 25{x^2}{y^2}z - 9{a^2}{b^2}z $
I'm not sure how to approach it. Any help would be appreciated
When it comes to factoring you just look at what is common to parts of the expression, in this case 25 and 9 do not have any common factors, so there is no integer value to factor out, and the variables are all unique except that both parts of the expression have a "z" so
$\displaystyle 25{x^2}{y^2}z - 9{a^2}{b^2}z=z(25x^2y^2-9a^2b^2)$
Now though, and this takes some insight, you may realize that $\displaystyle (25x^2y^2-9a^2b^2)$ is the difference of two perfect squares, and it is a well known fact that $\displaystyle (a^2-b^2)=(a+b)(a-b)$
So $\displaystyle (25x^2y^2-9a^2b^2)=(5xy+3ab)(5xy-3ab)$
and so the entire expression factors into $\displaystyle z(5xy+3ab)(5xy-3ab)$
We can start by pulling out the $\displaystyle z$.
$\displaystyle z(25{x^2}{y^2} - 9{a^2}{b^2}) $
Next, note the equation $\displaystyle a^2-b^2=(a-b)(a+b)$, in your case, $\displaystyle a=(5xy)^2$ and $\displaystyle b=(3ab)^2$.
Can you take it from here?
EDIT - Beat to the punch :P