If 2a -3b=3 & ab=2 , find the value of 8a3-27b3.

2a - 3b = 3
ab = 2
Find 8a3 - 27b
= (2a)3 - (3b)3   # of the form x3 - y3 = ( x- y)( ( x-y)2  +3xy )  x = 2a y = 3b
Thus
8a3 - 27b3   = (2a - 3b ) ( 2a - 3b)2 + 3(2a*3b) ) ) 
                   = (3)( 32 + 3(6*2 ) )
                   = (3)( 9 + 36) = 3*45 = 135

          

 

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