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# 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 $$(x + \frac{y}{10} )(x - \frac{y}{10} ).$$