Factoring x^2 - 8xy + 16y^2 - 25z^2

[fdragon]

What about something with 3 variables? How do I factor something like

x²-8xy+16y²-25z²

I see how the answer is (x-4y-5z)(x-4y+5z)

but I was thinking about what you just showed me and it wouldn't work here because there isn't anything constant. What else could you do other than guess and check (Cause it takes years!)? I'm again wondering if there is a way to select the right term to factor because in this case it is 16y² and not -8xy.... is there a way to determine that?

 

[tkhunny]

Re: Factoring 64a³+8

You must recognize patterns. You are asked to factor it, so it is likely to be possible.

There are various ways to proceed.

In this case, the three left terms look like a perfect square trinomial.

After rewriting that, it looks like a difference of squares.