Final answer:
This answer explains how to evaluate given expressions using identities.
Step-by-step explanation:
(i) To evaluate (2x - 1/x)², we can use the identity (a - b)² = a² - 2ab + b². Applying this identity, we have: (2x)² - 2(2x)(1/x) + (1/x)². Simplifying further, we get: 4x² - 4x + 1/x².
(ii) To evaluate (2x+y)(2x-y), we can use the identity (a + b)(a - b) = a² - b². Applying this identity, we have: (2x)² - (y)² = 4x² - y².
(iii) To evaluate (a²b - b²a)², we can use the identity (a - b)² = a² - 2ab + b². Applying this identity, we have: (a²b)² - 2(a²b)(b²a) + (b²a)² = a^4b^2 - 2a^2b^3 + b^4a².
(iv) To evaluate (a - 0.1)(a + 0.1), we can use the identity (a + b)(a - b) = a² - b². Applying this identity, we have: (a)² - (0.1)² = a² - 0.01.
(v) To evaluate (1.5x² - 0.3y²)(1.5x² - 0.3y²), we can use the identity (a - b)(a + b) = a² - b². Applying this identity, we have: (1.5x²)² - (0.3y²)² = 2.25x^4 - 0.09y^4.
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