Question

A student factored 24 x cubed y squared plus 8 xy as 8 xy left parenthesis 3 x squared y right parenthesis. What went? wrong? Factor correctly.

Answer 1

Start with

$24x^3y^2+8xy$

As for the numeric part, notice that 24 is a multiple of 8, so we can factor 8 out of both terms:

$24x^3y^2+8xy = 8(3x^3y^2+xy)$

Now, both $x$ and $y$ appear in both terms. We can factor them out:

$8(3x^3y^2+xy) = 8xy(3x^2y+1)$