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Simplify: $(x + y) (x + y + z)$

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

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

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

$y + x y + y z + x z$

answer is A.

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Detailed Solution

$(x + y) (x + y + z)$

$= x (x + y + z) + y (x + y + z)$

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

Collecting the like terms together, we get

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

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

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