Factorise the following :
`(i) 4x^(2)+20x+25 " " (ii) 9y^(2)-66yz+121z^(2) " " (iii) (2x+(1)/(3))^(2)-(x-(1)/(2))^(2)`

Explanation

(I ) `4x^(2)+20x+25=(2x)^(2)+2xx2xxx5+(5)^(2)`
`=(2x+5)^(2)` [using identity ,`a^(2)+2ab+b^(2)=(a+b)^(2)]`
(ii) `9y^(2)-66yz+121z^(2)=(3y)^(2)-2xx3yxx11z+(11z)^(2)`
`=(3y-11z)^(2)` [using identity ,`a^(2)-2ab+B^(2)=(a-b)^(2)`]
(iii) `(2x+(1)/(3))^(2)-(x-(1)/(2))^(2)=[(2x+(1)/(3))-(x-(1)/(2))][(2x+(1)/(3))+(x-(1)/(2))]`
[using identity ,` a^(2)-b^(2)=(a-b)(a+b)]`
`(2x-x+(1)/(3)=(1)/(2))(2x+x+(1)/(3)-(1)/(2))`
`(x+(2+3)/(6))(3x+(2-3)/(6))`
`=(x+(5)/(6))(3x-(1)/(6))`