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Simplify:(i) (x – y) (x + y) (x2 + y2) (x4 + y4)(ii) (2x – 1) (2x + 1) (4x2 + 1) (16x4 + 1) |
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Answer» (i) (x – y) (x + y) (x2 + y2) (x4 + y4) = (x2 – y2) (x2 + y2) (x4 + y4) = [(x2)2 – (y2)2] (x4 + y4) = (x4 – y4) (x4 – y4) = [(x4)2 – (y4)2] = x8 – y8 (ii) (2x – 1) (2x + 1) (4x2 + 1) (16x4 + 1) = [(2x)2 – (1)2] (4x2 + 1) (16x4 + 1) = (4x2 – 1) (4x2 + 1) (16x4 + 1) 1 = [(4x2)2 – (1)2] (16x4 + 1) 1 = (16x4 – 1) (16x4 + 1) 1 = [(16x4)2 – (1)2] 1 = 256x8 – 1 |
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