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Factorisation - Factorisation Using Identities

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We know that ,
`(a + b)^2  = a^2 + 2ab + b^2`       (I) 
`(a – b)^2  = a^2 – 2ab + b^2`       (II) 
`(a + b) (a – b)  = a^2 – b^2`          (III)  

Example : Factorise `4y^2 – 12y + 9`
Solution :  Observe `4y^2 = (2y)^2`, `9 = 3^2` and `12y = 2 × 3 × (2y)`
Therefore,
`4y^2 – 12y + 9 = (2y)^2 – 2 × 3 × (2y) + (3)^2` .... [Using identity II ]
= `(2y – 3)^2`      ...(required factorisation) 

Example : Factorise  `49p^2 – 36`
Solution :  There are two terms; both are squares and the second is negative. The expression is of the form `(a^2 – b^2)`.
Identity III is applicable here ; 
`49p^2  – 36 = (7p)^2 – (6)^2`
= (7p – 6 ) ( 7p + 6)                     ....(required factorisation) 

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