question_answer

  Using a suitable identity to get the product \[\left( 3x-\frac{1}{3} \right)\left( 3x-\frac{1}{3} \right)\].

Answer:

Using the identity \[{{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}},\] We have,  \[\left( 3x-\frac{1}{3} \right)\left( 3x-\frac{1}{3} \right)={{\left( 3x-\frac{1}{3} \right)}^{2}}\] \[={{(3x)}^{2}}-2(3x)\left( \frac{1}{3} \right)+{{\left( \frac{1}{3} \right)}^{2}}\] \[=9{{x}^{2}}-2x+\frac{1}{9}.\]