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Evaluate:(i) \(({2x-1\over x})^2\)(ii) (2x + y) (2x – y)(iii) (a2b – b2a)2(iv) (a – 0.1) (a + 0.1) (v) (1.5.x2 – 0.3y2) (1.5x2 + 0.3y2) |
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Answer» (i) \(({2x-1\over x})^2\) \(= ({2x-1\over x})^2\) = (2x)2 + (\(1\over x\))2 – 2 (2x)(\(1\over x\)) [(a – b)2 = a2 + b2 – 2ab] = \(4x^2 + 1 \over x^2 - 4\) (ii) (2x + y) (2x – y) (2x + y) (2x – y) [(a – b)(a + b) = a2 – b2] = (2x )2 – (y)2 = 4x2 – y2 (iii) (a2b – b2a)2 (a2b – b2a)2 [(a – b)2 = a2 + b2 – 2ab] = (a2b)2 + (b2a)2 – 2 (a2b)( b2a) = a4b2 + b4a2 – 2a3b3 (iv) (a – 0.1) (a + 0.1) (a – 0.1) (a + 0.1) [(a – b)(a + b) = a2 – b2 ] = (a)2 – (0.1)2 = (a)2 – 0.01 (v) (1.5 x2 – 0.3y2) (1.5 x2 + 0.3y2) (1.5 x2 – 0.3y2) (1.5x2 + 0.3y2) [(a – b)(a + b) = a2 – b2 ] = (1.5 x2)2 – (0.3y2)2 = 2.25 x4 – 0.09y4 |
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