# 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

(ii) 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

(iii) L.H.S = ( - )2 + 2mn

= ( )2 + ( )2 – 2mn + 2mn

= ( )2 + ( )2

= m2 + n2

= R.H.S

Hence, verified

(iv) 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

(v) 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

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