Evaluate the following using identities:
v. $(1.5 x^{2} - 0.3 y^{2}) (1.5 x^{2} + 0.3 y^{2})$

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Solution

Given: $(1.5 x^{2} - 0.3 y^{2}) (1.5 x^{2} + 0.3 y^{2})$

Using the identity, $(a - b) (a + b) = a^{2} - b^{2}$

$∴ (1.5 x^{2} - 0.3 y^{2}) (1.5 x^{2} + 0.3 y^{2}) = (1.5 x^{2})^{2} - (0.3 y^{2})^{2} = 2.25 x^{4} - 0.09 y^{4}$

Hence, $(1.5 x^{2} - 0.3 y^{2}) (1.5 x^{2} + 0.3 y^{2}) = 2.25 x^{4} - 0.09 y^{4}$

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