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Which of these is NOT an identity (true for every value of the variables)?

Class 9Algebraic IdentitiesPolynomials

A $(x + y) (x - y) = x^{2} - y^{2}$
B $(x + y)^{2} = x^{2} + y^{2}$
C $(x - y)^{2} = x^{2} - 2 x y + y^{2}$
D $(x + 1) (x + 2) = x^{2} + 3 x + 2$

Step-by-Step Solution

Try

x = y = 1 : (1 + 1)^{2} = 4

but

1^{2} + 1^{2} = 2

. The

2 x y

term is missing, so it is not an identity.

Answer: B)

(x + y)^{2} = x^{2} + y^{2}

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