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Factorisation - Factorisation Using Identities

notes

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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Factorizing using Identities [00:57:38]
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