(i) 64x6 – 729y6
Above terms can be written as,
(2x)6 – (3y)6
[(2x)2]3 – [(3y)2]3
We know that, a3 – b3 = (a – b) (a2 + ab + b2)
So, a = (2x)2, b = (3y)2
[(2x)2 – (3y)2] [((2x)2)2 + ((2x)2× (3y)2) + ((3y)2)2]
(4x2 – 9y2) [16x4 + (4x2 × 9y2) + (9y2)2]
(4x2 – 9y2) [16x4 + 36x2y2 + 81y4] [(2x)2 – (3y)2] [16x4 + 36x2y2 + 81y4]
(2x + 3y) (2x – 3y) (16x4 + 36x2y2 + 81y4)
(ii) x3 – (8/x)
Above terms can be written as,
(1/x) (x3 – 8)
(1/x) [(x)3 – (2)3]
We know that, a3 – b3 = (a – b) (a2 + ab + b2)
So, a = x, b = 2
(1/x) (x – 2) (x2 + 2x + 4)
More Solutions:
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