# How do you factor # x^2 - 8xy + 16y^2 - 3x + 12y +2#?

##### 1 Answer

#x^2-8xy+16y^2-3x+12y+2=(x-4y-1)(x-4y-2)#

#### Explanation:

This is a disguised version of:

#t^2-3t+2 = (t-1)(t-2)#

with

#x^2-8xy+16y^2-3x+12y+2#

#=(x-4y)^2-3(x-4y)+2#

#=((x-4y)-1)((x-4y)-2)#

#=(x-4y-1)(x-4y-2)#

**A Little Slower**

This polynomial is a mixture of terms of degree

So if it factors, then it has two factors each containing a mixture of terms of degree

If we removed the terms of degree

So to find the terms of degree

#x^2-8xy+16y^2#

Note that

#x^2-8xy+16y^2 = (x-4y)^2#

Next note that the terms of degree

Hence we find:

#x^2-8xy+16y^2-3x+12y+2 = (x-4y)^2-3(x-4y)+2#

Then substitute