Show that (4pq + 3q)2 - (4pq - 3q)2 = 48pq2           

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126.

Show that

(4pq + 3q)2 - (4pq - 3q)2 = 48pq2    


         


LHS       = (4pq + 3q)2 - (4pq - 3q)2 = 48pq2
            = [(4pq)2 + 2(4pq)(3q) + (3q)2 ]   -[(4pq)2 - 2(4pq)(3q) + (3q)2 ]
            = 16p2q2 + 24pq2 + 9q2 - (16p2q2 - 24pq2 + 9q2 ]
            = (16 - 26)p2q2 + (24 + 24)pq2 + (9 -9)q2
            = (0)p2q2 + 48pq2 + (0)q2
            = 48pq2 = RHS

Since, LHS = RHS

∴      (4pq + 3q)2 - (4pq - 3q)2 = 48pq2

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