Show that:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(i) 
L.H.S = (3x + 7)2 – 84x
= (3x)2 + (7)2 + 2 (3x) (7) – 84x
= (3x)2 + (7)2 + 42x – 84x
= (3x)2 + (7)2 – 42x
= (3x)2 + (7)2 – 2 (3x) (7)
= (3x – 7)2
= R.H.S
Hence, proved
L.H.S = (9a – 5b)2 + 180ab
= (9a)2 + (5b)2 – 2 (9a) (5b) + 180ab
= (9a)2 6 (5b)2 – 90ab + 180ab
= (9a)2 + (5b)2 + 9ab
= (9a)2 + (5b)2 + 2 (9a) (5b)
= (9a + 5b)2
= R.H.S
Hence, proved
L.H.S = (
- 
)2 + 2mn
= (
)2 + (
)2 – 2mn + 2mn
= (
)2 + (
)2
= 
m2 + 
n2
= R.H.S
Hence, verified
L.H.S = (4pq + 3q)2 – (4pq – 3q)2
= (4pq)2 + (3q)2 + 2 (4pq) (3q) – (4pq)2 – (3q)2 + 24pq2
= 24pq2 + 24pq2
= 48pq2
Hence, proved
L.H.S = (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a)
Using identity:
(a – b) (a + b) = a2 – b2
We get,
= (a2 – b2) + (b2 – c2) + (c2 – a2)
= a2 – b2 + b2 – c2 + c2 – a2
= 0
= R.H.S
Hence, verified