Answer:
(x - y + 3)(x + y - 7)
Explanation:
x^2 - 4x - 21 + 10y - y^2
= x^2 - y^2 +10y - 4x - 21
= (x - y)(x + y) + 10y - 4x - 21
This is a stab in the dark - I think this might factor to (x - y + 3)(x + y - 7) or
(x - y - 7)(x + y + 3) - I think I've come across one like this before.
Lets try the first one:
(x - y + 3)(x + y - 7) = x^2 + xy - 7x - y^2 - xy +3y + 3x + 7y - 21
= x^2 -7x + 3x -21 + 10y - y^2.
This is correct but isn't a very logical way to do this. There must be a better way!
The logical way is by reducing the expression to the difference of 2 squares: (x - 2)^2 - (y - 5)^2
This factors to ( x + y -7)(x - y + 3).