(i) z2 – 16
z2 – 16 = z2 – 42
We have a2 – b2 = (a + b) (a – b)
Let a = z and b = 4,
z2 – 42 = (z + 4) (z – 4)
(ii) 9 – 4y2
9 – 4y2 = 32 – 22 y2
= 32 – (2y)2
Let a = 3 and b = 2y, then
a2 – b2 = (a + b) (a – b)
∴ 32 – (2y)2 = (3 + 2y) (3 – 2y)
9 – 4y2 = (3 + 2y) (3 – 2y)
(iii) 25a2 – 49b2
25a2 – 49b2 = (5a)2 – (7b)2
Let A = 5a and B = 7b
A2 B2
(5a)2 – (7b)2 = (5a + 7b) (5a – 7b)
(iv) x4 – y4
Let x4 – y4 = (x2)2 – (y2)2
We have a2 – b2 = (a + b) (a – b)
(x2)2 – (y2)2 = (x2 + y2) (x2 – y2)
x4 – y4 = (x2 + y2) (x2 – y2)
Again we have x2 – y2 = (x + y) (x – y)
∴ x4 – y4 = (x2 + y2) (x + y) (x – y)