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3.Factorize the following using appropriate identities :
i)\(9x^2 + 6xy + y^2\)
ii)\(4y^2 - 4y + 1\)
iii)\(x^2 - y^2/100\)
Answer :

i)\(9x^2 + 6xy + y^2 = {3x}^2 + 2(3x)(y) + {y}^2\).....by using identity, \((a + b)^2 = a^2 + 2ab + b^2\)
= (3x + y)^2
Therefore, the factors are (3x + y)(3x + y).

ii)\(4y^2 - 4y + 1 = {2y}^2 - 2(2y)(1) + {1}^2\).....by using identity, \((a + b)^2 = a^2 + 2ab + b^2\)
= (2y - 1)^2
Therefore, the factors are (2y - 1)(2y - 1).

iii)\(x^2 - y^2/100 = (x + y/10)(x - y/10)\).....by using identity, \((a^2 - b^2) = (a + b)(a - b))\)
= (x + y/10)(x - y/10)
Therefore, the factors are (x + y/10)(x - y/10).