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Algebraic Identities

x+y+z2=

Question

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

A

x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 x z

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B

x^{2} - y^{2} + z^{2} + 2 x y + 2 y z + 2 x z

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C

x^{2} - y^{2} - z^{2} - 2 x y - 2 y z - 2 x z

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D

None of the above

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Solution

The correct option is A $x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 x z$
$(x + y + z)^{2} = (x + y + z) (x + y + z)$
$= x (x + y + z) + y (x + y + z) + z (x + y + z)$
$= x^{2} + x y + x z + x y + y^{2} + y z + x z + y z + z^{2}$
$= x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 x z$

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