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Evaluate each of the following using identities:(i) \((2x-\frac{1}{x})^2\)(ii) (2x+y) (2x - y)(iii) (a2b - b2a)2(iv) (a – 0.1) (a +0.1)(v) (1.5x2 - 0.3y2)(1.5x2 - 0.3y2) |
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Answer» (i) We know, (a - b)2 = a2 + b2 -2ab Here, a = 2x and b = \(\frac{1}{x}\) \((2x-\frac{1}{x})^2\) = \((2x)^2-(\frac{1}{x})^2 - 2\times x\times \frac{1}{x}\) = \((4x)^2-(\frac{1}{x})^2 - 2\) (ii) We know, (a-b)2 = (a+b) (a - b) (2x+y)(2x-y) = (2x)2– y2 = 4x2 – y2 (iii) We know, (a - b)2 = a2 + b2 - 2ab Here, (a2b - b2a)2 = (a2b)2 + (b2a)2 - 2 x a2b x b2a = a4b2 + a2b4 - 2a3b3 (iv) We know, (a-b)2 = (a+b) (a - b) (a – 0.1)(a +0.1) = (a)2– (0.1)2 = a2 – 0.01 (v) We know, (a - b)2 = a2 - b2 (1.5x2 - 0.3y2)(1.5x2 - 0.3y2) = (1.5x2)2 - (0.3y2)2 = 2.25x4 - 0.09y4 |
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