Question

factoring :
x^{2}-8xy+16y^{2}-3x+12y+2

Answer 1

\[ (-2+x-4 y) (-1+x-4 y) \]

Answer 2

how did you get that answer?

Answer 3

One way to see it is to note that:\[x^2-8xy+16y^2 = x^2-2(x)(4y)+(4y)^2 = (x-4y)^2\]and also:\[-3x+12y = -3(x-4y)\]So we really have:\[(x-4y)^2-3(x-4y)+2\]This is a quadratic in terms of z = x - 4y.

Answer 4

i never understand how to factor...

Answer 5

I believe this type of factoring problem with two or more independent variable has no fixed rule, just few gimmicks ;)

Answer 6

Please note there exists algorithms to do this but my earlier comment is for a paper pencil approach only.