Which of the following algebraic identities are correctly written?

(x + a) (x + b) = x^{2} + (a + b) x + a b

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a^{2} + b^{2} = (a + b) (a - b)

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(a - b)^{2} = a^{2} - 2 a b + b^{2}

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

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Solution

The correct options are
A $(x + a) (x + b) = x^{2} + (a + b) x + a b$
C $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
D $(x + y)^{2} = x^{2} + 2 x y + y^{2}$
An identity is an equality, which is true for all values of the variables in the equality.

Some of the algebraic identites are:

$(x + a) (x + b) = x^{2} + (a + b) x + a b$
$a^{2} - b^{2} = (a + b) (a - b)$
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$(x + y)^{2} = x^{2} + 2 x y + y^{2}$

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