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Evaluate each of the following using identities:
$(1.5.x^2 - 0.3y^2) (1.5x^2 + 0.3y^2)$
Given:
$(1.5.x^2 - 0.3y^2) (1.5x^2 + 0.3y^2)$
To do:
We have to evaluate the given expression using a suitable identity.
Solution:
We know that,
$(a+b)^2=a^2+b^2+2ab$
$(a-b)^2=a^2+b^2-2ab$
$(a+b)(a-b)=a^2-b^2$
Therefore,
$(1.5 x^{2}-0.3 y^{2})(1.5 x^{2}+0.3 y^{2})=(1.5 x^{2})^{2}-(0.3 y^{2})^{2}$
$=2.25 x^{4}-0.09 y^{4}$
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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