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Question 2: Factorize a 2/ b 2 − 2 + b 2 /a 2

Question 2: Factorize    \frac{a ^{2}}{ b^{2}}-2+ \frac{ b^{2}}{a ^{2}}

Factorizing an expression —

Solution:

 

 

Given expression is

\frac{a ^{2}}{ b^{2}}-2+ \frac{ b^{2}}{a ^{2}}

This can be written as;

= (\frac{a}{b})^{2}-2+ (\frac{b}{a})^{2}

We convert it to  a^{2}-2(a)(b)+ b^{2}= (a-b)^{2}  form;

=  (\frac{a}{b})^{2}-2(\frac{a}{b})(\frac{b}{a})+ (\frac{b}{a})^{2}

 =(\frac{a}{b}-\frac{b}{a})^{2}

 

Because as per formula here

\frac{a}{b}  stands for ‘a’

and

\frac{b}{a} stands for ‘b’

and so

(\frac{a}{b}-\frac{b}{a}) stands for (a-b)

 

 


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