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Examples 4 to 6
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(4) If m = – 28, and n = 20, find the value of 9m2 + 24mn + 16n2.
Soln. 9m2 + 24mn + 16n2 = ( 3m + 4n )2 = ( – 84 + 80 )2 = 16.
(5) Evaluate : 123 + 253 – 373
Soln. Let, a = 12, b = 25 & c = – 37
a + b + c = 0
123 + 253 – 373
= a3 + b3 + c3
= 3 abc ( a + b + c = 0 )
= 3 ( 12 ) ( 25 ) ( – 37 ) = 33300.
(6) If a = 0.572, b = 0.032, c = 0.604, find the value of a3 + b3 – c3 + 3abc.
Soln. a3 + b3 – c3 + 3abc
= a3 + b3 + ( – c3 ) + 3abc
= – 3abc + 3abc ( a + b + ( – c ) = 0.572 + 0.032 – 0.604 = 0 )
= 0
