Evaluate each of the following using identities:

Question:

Evaluate each of the following using identities:

(i) $(2 x-1 / x)^{2}$

(ii) $(2 x+y)(2 x-y)$

(iii) $\left(a^{2} b-a b^{2}\right)^{2}$

(iv) $(a-0.1)(a+0.1)$

(v) $\left(1.5 x^{2}-0.3 y^{2}\right)\left(1.5 x^{2}+0.3 y^{2}\right)$

Solution:

(i) Given,

$(2 x-1 / x)^{2}=(2 x)^{2}+(1 / x)^{2}-2 * 2 x * 1 / x$

$(2 x-1 / x)^{2}=4 x^{2}+1 / x^{2}-4 \quad\left[\therefore(a-b)^{2}=a^{2}+b^{2}-2 a b\right]$

Where, $a=2 x, b=1 / x$

$\therefore(2 x-1 / x)^{2}=4 x^{2}+1 / x^{2}-4$

(ii) Given,

$(2 x+y)(2 x-y)$

$=(2 x)^{2}-(y)^{2} \quad\left[\therefore(a+b)(a-b)=a^{2}-b^{2}\right]$

$=4 x^{2}-y^{2}$

$\therefore(2 x+y)(2 x-y)=4 x^{2}-y^{2}$

(iii) Given, 

(iv)  Given,

 

 

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