Factorise the following using appropriate identities:
Factorise the following using appropriate identities:
(i) 9x2 + 6xy + y2 (ii) 4y2 - 4y + 1 (iii) x2 - y2/100
Answer
(i) 9x2 + 6xy + y2 = (3x) 2 + (2×3x×y) + y2
Using identity, (a + b)2 = a2 + 2ab + b2
Here, a = 3x and b = y
9x2 + 6xy + y2 = (3x) 2 + (2×3x×y) + y2 = (3x + y)2 = (3x + y) (3x + y)
(ii) 4y2 - 4y + 1 = (2y)2 - (2×2y×1) + 12
Using identity, (a - b)2 = a2 - 2ab + b2
Here, a = 2y and b = 1
4y2 - 4y + 1 = (2y)2 - (2×2y×1) + 12 = (2y - 1)2 = (2y - 1) (2y - 1)
(iii) x2 - y2/100 = x2 - (y/10)2
Using identity, a2 - b2 = (a + b) (a - b)
Here, a = x and b = (y/10)
x2 - y2/100 = x2 - (y/10)2 = (x - y/10) (x + y/10)
