# Factorise : (a – 3b)2 – 36 b2

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Factorise : (i) (a – 3b)2 – 36 b2

(ii) 25 (a – 5b)2 – 4 (a – 3b)2

(iii) a2 – 0.36b2

(iv) a4 – 625

(v) x4 – 5x2 – 36

(vi) 15 (2x – y)2 – 16 (2x – y) – 15

answered May 23 by (-1,379 points)

(i) (a – 3b)2 – 36 b2

= (a – 3b)2 – (6b)2

= (a – 3b + 6b) (a – 3b – 6b)

= {a2 – b2 = (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)

{a2 – b2 = (a + b) (a – b)

= (7a = 31b) (3a – 91b)

(iii) a2 – 0.36 b2

= (a)2 – (0.6b)2

= (a + 0.6b) (a – 0.6b)

{a2 – b2 = (a + b) (a – b)

(iv) a4 – 625 = (a2)2 – (25)2

= (a2 + 25) (a2 – 25)

{a2 – b2 = (a + b) (a – b)}

= (a2 + 25) {(a)2 – (5)2}

= (a2 + 25) (a + 5) (a – 5)

(v) x4 – 5x2 – 36

= (x2)2 – 5x2 - 36

= (x2)2 – 9x2 + 4x2 – 36

= x2 (x2 – 9) + 4 (x2 – 9)

= (x2 – 9) + (x2 + 4)

= {x2 – (3)2} {x2 + 4)

= (x + 3) (x – 3) (x2 + 4)

= (x2 + 4) (x + 3) (x – 3)

(vi) 15 (2x – y)2 – 16 (2x – y) – 15

let 2x – y = a, then

15a2 – 16a - 15

= 15a2 – 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)