Factorize the following using appropriate identities :
i)\(9x^2 + 6xy + y^2\)
ii)\(4y^2 - 4y + 1\)
iii)\(x^2 - \frac{y^2}{100} \)

i) \(9x^2 + 6xy + y^2 \)
\( = {3x}^2 + 2(3x)(y) + {y}^2\)
\([\because (a + b)^2 = a^2 + 2ab + b^2\)
\( = (3x + y)^2 ] \)

Therefore, the factors are (3x + y)(3x + y).


ii) \(4y^2 - 4y + 1 \)
\( = {2y}^2 - 2(2y)(1) + {1}^2\)
\([\because (a + b)^2 = a^2 + 2ab + b^2\)
\( = (2y - 1)^2 ]\)

Therefore, the factors are (2y - 1)(2y - 1).


iii)\(x^2 - \frac{y^2}{100} \)
\( = (x +\frac{y}{10} )(x - \frac{y}{10} )\)
\([\because (a^2 - b^2) = (a + b)(a - b))] \)
\( =(x + \frac{y}{10} )(x - \frac{y}{10} ) \)

Therefore, the factors are \( (x + \frac{y}{10} )(x - \frac{y}{10} ). \)