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Question

Show that:
(9p5q)2+180pq=(9p+5q)2


Solution

L.H.S = (9p5q)2+180pq
=(9p)22×9p×5q+(5q)2+180pq
[Using identity (ab)2=a22ab+b2]
=81p290pq+25q2+180pq
=81p2+90pq+25q2
=(9p)2+2×9p×5q+(5q)2
=(9p+5q)2             [(a+b)2=a2+2ab+b2]
Hence, (9p5q)2+180pq=(9p+5q)2 Proved


Mathematics
NCERT Textbook
Standard VIII

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