Factorise the following expressions.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii)
(Hint: Expand 
first)
(viii)
(i) a2 + 8a + 16
= a2 + 2× a × 4 + 42
Using identity (a + b)2 = a2 + 2ab + b2
Here a =a; b = 4
a2 + 2× a × 4 + 42
= (a + 4)2
= (a + 4)(a + 4)
(ii) p2 -10p + 25
= p2 - 2× 5 × p + 52
Using identity (a - b)2 = a2 - 2ab + b2
Here a =p; b = 5
p2 - 2× 5 × p + 52
= (p - 5)2
= (p-5)(p-5)
(iii) 25m2 + 30m + 9
= (5m)2 + 2 × 5 × 3 × m + 32
Using identity (a + b)2 = a2 + 2ab + b2
Here a =5m; b = 3
(5m)2 + 2 × 5 × 3 × m + 32
= (5m + 5)2
= (5m + 5)(5m + 5)
(iv) 49y2 + 84yz + 36z2
= (7y)2 + 2 × 7 × 6 × y × z + (6z)2
Using identity (a + b)2 = a2 + 2ab + b2
Here a =7y; b = 6z
(7y)2 + 2 × 7 × 6 × y × z + (6z)2
= (7y + 6z)2
= (7y + 6z)(7y + 6z)
(v) 4x2 - 8x + 4
= (2x)2 - 2 × 2 × 2× x + 22
Using identity (a - b)2 = a2 - 2ab + b2
Here a =2x; b = 2
(2x)2 - 2 × 2 × 2× x + 22
= (2x - 2)2
= (2x - 2)(2x - 2)
(vi) 121b2 - 88bc + 16c2
= (11b)2 - 2 × 11b × 4c + (4c)2
Using identity (a - b)2 = a2 - 2ab + b2
Here a =11b; b = 4c
(11b)2 - 2 × 11b × 4c + (4c)2
= (11b – 4c)2
= (11b – 4c)(11b – 4c)
(vii) (l + m)2 - 4lm
Expand (l + m)2 = l2 + 2lm + m2
[using (a + b)2 = a2 + 2ab + b2]
l2 + 2lm + m2 - 4lm
⇒ l2 - 2lm + m2
= l2 - 2 × l × m + m2
Using identity (a - b)2 = a2 - 2ab + b2
Here a =l; b = m
l2 - 2 × l × m + m2
= (l – m)2
= ( l - m)(l - m)
(viii) a⁴ + 2a2b2 + b⁴
= (a2)2 + 2 × a2 × b2 + (b2)2
Using identity (a + b)2 = a2 + 2ab + b2
Here a = a2; b = b2
(a2)2 + 2 × a2 × b2 + (b2)2
= (a2 + b2)2
= (a2 + b2)(a2 + b2)