Answer :

(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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