Question

(2a + 3)² = 2a² + 6a + 9, Find the errors and correct the given mathematical sentence.

Answer 1

Identity : ( a + b )² = a² + b² + 2ab


According to the identity,


=> ( 2a + 3)²

=> ( 2a )² + ( 3 )² + 2( 2a × 3 )

=> 4a² + 9 + 12a [ correct equation ]





$\mathbf{Errors} : \: \\ \\ \\ \bold{ {2}^{2} was \: \: \: written \: \: wrong \: \: as \: 2 \: \: but \: \: it \: \: is \: \: 4 \: } \: \\ \\ \mathbf{ Identity \: \: includes \: \: 2ab \: \: \: i.e. \: \: 2(2a×3)= 12a \: \: \: and \: \: this \: is \: \: also \: \: written \: \: as \: \: 6a \: Where \: \: value \: \: of \: \: 2 is \: \: not \: \: included}$

Answer 2

Solution :

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By algebraic identity :

( x + y )² = x² + 2xy + y²

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Here ,

x = 2a , y = 3

( 2a + 3 )² = (2a)² + 2×2a×3 + 3²

= 4a² + 12a + 9

But , in the given problem

( 2a + 3 )² = 2a² + 6a + 9

First term and second terms in RHS

part is wrong .

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