(i) (a – 3b)^{2 }– 36 b^{2}
= (a – 3b)^{2} – (6b)^{2 }
= (a – 3b + 6b) (a – 3b – 6b)
= {a^{2} – b^{2 }= (a + b) (a – b)}
= (a + 3b) (a – 9b)
(ii) 25 (a – 5b)^{2 }– 4 (a – 3b)^{2}
= [5 (a – 5b)]^{2 }– [2 (a – 3b)]2
= (5a – 25b)2 – (2a – 6b)^{2 }
= (5a – 25b + 2a – 6b) (5a – 25b – 2a + 6b)
{a^{2} – b^{2 }= (a + b) (a – b)
= (7a = 31b) (3a – 91b)
(iii) a^{2} – 0.36 b^{2}
= (a)^{2} – (0.6b)^{2}
= (a + 0.6b) (a – 0.6b)
{a^{2} – b^{2} = (a + b) (a – b)
(iv) a^{4} – 625 = (a^{2})^{2} – (25)^{2}
= (a^{2 }+ 25) (a^{2} – 25)
{a^{2} – b^{2} = (a + b) (a – b)}
= (a^{2} + 25) {(a)^{2} – (5)^{2}}
= (a^{2} + 25) (a + 5) (a – 5)
(v) x^{4 }– 5x^{2} – 36
= (x^{2})^{2} – 5x^{2} - 36
= (x^{2})^{2} – 9x2 + 4x2 – 36
= x^{2} (x^{2} – 9) + 4 (x^{2} – 9)
= (x^{2} – 9) + (x^{2} + 4)
= {x^{2} – (3)^{2}} {x^{2} + 4)
= (x + 3) (x – 3) (x^{2} + 4)
= (x^{2} + 4) (x + 3) (x – 3)
(vi) 15 (2x – y)^{2} – 16 (2x – y) – 15
let 2x – y = a, then
15a^{2} – 16a - 15
= 15a^{2} – 25a + 9a – 15
= 5a (3a – 5) + 3 (3a - 5)
= (3a – 5) (5a + 3)
[3 (2x – y) – 5] [5 (2x – y) + 3]
= (6x – 3y – 5) (10x – 5y + 3)