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प्रश्न
Factorise the following using suitable identity
a2 + 6ab + 9b2 – c2
उत्तर
a2 + 6ab + 9b2 – c2 = a2 + 2 × a × 3b + 32b2 – c2
= a2 + (2 × a × 3b) + (3b)2 – c2
This expression is of the form of identity
[a2 + 2ab + b2] – c2 = (a + b)2 – c2
a2 + (2 × a × 3b) + (3b)2 – c2 = (a + 3b)2 – c2
Again this R.H.S is of the form of identity
a2 – b2 = (a + b)(a – b)
(a + 3b)2 – c2 = [(a + 3b) + c][(a + 3b) – c]
a2 + 6ab + 9b2 – c2 = (a + 3b + c)(a + 3b – c)
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