# How do you factor 92x^10y^4 - 54x^12y^9?

Mar 27, 2015

Start by taking out any common factors:

There are 'obvious' common factors of $2$, some power of $x$ and some power of $y$. Take those out.
(I say "take them out", because I can always imagine parentheses around the expression. Taking out a common factor is "undistributing" the factor.)

$\left(92 {x}^{10} {y}^{4} - 54 {x}^{12} {y}^{9}\right) = 2 {x}^{10} {y}^{4} \left(46 - 27 {x}^{2} {y}^{5}\right)$

Now we need to ask ourselves if we can factor $46 - 27 {x}^{2} {y}^{5}$.

Are there any common factors? None that i see.
Is it a special product? Not that I recognize.
Can it be factored by trial and error? I only know how to do that for trinomials (3 terms)

Well, then I'll have to give the hardest answer for students to give: "We're done. This can be factored no further."
((Whispers) unless there's something I've forgotten or haven't learned yet.)

(It's hard for students, because students are frequently reminded that there are tricks (techniques) they don't know yet or have forgotten. That's normal. But when you think you're daon, say "That's it, I'm done")