\[{x}^{2}+2xy-8{y}^{2}\]
1
In general, given ax2+bx+ca{x}^{2}+bx+c, the factored form is:
a(x−−b+b2−4ac2a)(x−−b−b2−4ac2a)a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})

2
In this case, a=1a=1, b=2yb=2y and c=−8y2c=-8{y}^{2}.
(x−−2y+(2y)2−4×−8y22)(x−−2y−(2y)2−4×−8y22)(x-\frac{-2y+\sqrt{{(2y)}^{2}-4\times -8{y}^{2}}}{2})(x-\frac{-2y-\sqrt{{(2y)}^{2}-4\times -8{y}^{2}}}{2})

3
Simplify.
(x−2y)(x+4y)(x-2y)(x+4y)

Done
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