a) x2 + 4x - 45
= (x2 - 5x) + (9x - 45)
= x(x - 5) + 9(x - 5)
= (x + 9)(x - 5)
b) x2 - 12xy - 13y2
= (x2 - 13xy) + (xy - 13y2)
= x(x - 13y) + y(x - 13y)
= (x + y)(x - 13y)
c) 16 - x2 - 2xy - y2
= 16 - (x2 + 2xy + y2)
= 42 - (x + y)2
= (4 - x - y)(4 + x + y)
d) x - 2y + x2 - 4y2
= (x - 2y) + (x2 - 4y2)
= (x - 2y) + (x - 2y)(x + 2y)
= (x - 2y)(x + 2y + 1)