Step 1 :Factor the given expression: $x^{2}+4 x y-21 y^{2}$
Step 2 :Find the factors of the constant term (-21) and check if they satisfy the middle term (4x): $(x-3 y)(x+7 y)$
Step 3 :\( \boxed{(x-3 y)(x+7 y)} \)