a) 9 + 10ab - a2 - 25b2 = 9 - (a2 - 10ab + 25b2)
= 9 - (a - 5b)2
= (3 - a + 5b)(3 + a - 5b)
b) 16x2 - (x2 - 2x + 1) = 16x2 - (x - 1)2
= (4x - x + 1)(4x + x - 1)
= (3x + 1)(5x - 1)
d) 12xy2 + 27y2 - 3y3 - 12x2 = 3(4xy2 + 9y2 - y3 - 4x2)
f) x4 + 64y4 = x4 + 16x2y2 + 64y4 - 16x2y2
= (x2 + 8y2)2 - 16x2y2
= (x2 - 4xy + 8y2)(x2 + 4xy + 8y2)