Substitute a new variable for the common term.

Let $x = a+y$.
The expression becomes:

$$x^2 - 11x - 42$$

We need to find two numbers that multiply to $-42$ and add up to $-11$. These numbers are 3 and $-14$.
So, we can rewrite the middle term:

$$x^2 + 3x - 14x - 42$$

Group the terms and factor:

$$x(x+3) - 14(x+3)$$

Factor out the common binomial $(x+3)$:

$$(x+3)(x-14)$$

Now, replace $x$ with $(a+y)$:

$$((a+y)+3)((a+y)-14)$$