Verified answer

The first 3 terms form a perfect trinomial, so:

x² + 2xy + y² - 16

= (x + y)² - 16

Now we have a difference of squares, so:

(x + y)² - 16

= (x + y + 4)(x + y - 4)

Well x^2 + 2xy + y^2 = (x + y)^2 so you have the difference of squares, (x + y)^2 - 4^2

Use the difference of squares formula a^2 - b^2 = (a + b)(a - b) where a = x + y and b = 4

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

=(x + y)^2 - 16

=[(x + y) + 4][(x + y) - 4]

=(x + y + 4)(x + y - 4) answer//