PLEASE ELABORATE
a2-(b-c)2
Answers
Answer:
(i) a2 – (b – c)2
= (a – (b – c)) (a + b – c)
[a2 – b2 = (a – b) (a + b)]
= (a – b + c) (a + b – c)
(ii) 25 (2x – y)2 – 16 (x – 2y)2
= (5 (2x – y)2 – (4 (x – 2y))2
= [5(2x – y) – 4 (x – 2y)] [5 (2x – y) + 4 (x – 2y)
= [10x – 5y – 4x + 8y] [10x – 5y + 4x – 8y]
[a2 – b2 = (a – b) (a + b)
= (6x + 3y) (14x – 13y) = 3 (2x + y) (14x – 13y)
(iii) 16 (5x + 4)2 – 9 (3x – 2)2
= (4 (5x + y))2 – (3 (3x – 2))2
= [4 (5x + 4) – 3 (3x – 2)] [4 (5x + 4) + 3 (3x – 2)]
[a2 – b2 = (a – b) (a + b)]
= (20x + 16 – 9x + 6] [20x + 16 + 9x – 6]
= [11x + 22] (29x + 10) = 11 (x + 2) (29x + 10)
(iv) 9x2 – (1/16) = (3x)2 – (1/4)2
= (3x – (1/4)) (3x + (1/4)) [(a2 – b2) = (a – b) (a + b)]
(v) 25 (x – 2y)2 – 4 = (5 (x – 2y))2 – 22
= [5 (x – 2y) – 2] [5 (x – 2y) + 2]
[a2 – b2 = (a – b) (a + b)]
= (5x – 10y – 2) (5x – 10y + 2)