Simplify (x+y+z)^2

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

Step 1

Rewrite ${(x + y + z)}^{2}$ as $(x + y + z) (x + y + z)$ .

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

Step 2

Expand $(x + y + z) (x + y + z)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x + x y + x z + y x + y \cdot y + y z + z x + z y + z \cdot z$

Step 3

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $y$ by $y$ .

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

Multiply $z$ by $z$ .

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

Step 4

Add $x y$ and $y x$ .

Reorder $y$ and $x$ .

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

Add $x y$ and $x y$ .

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

Step 5

Add $x z$ and $z x$ .

Reorder $z$ and $x$ .

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

Add $x z$ and $x z$ .

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

Step 6

Add $y z$ and $z y$ .

Reorder $z$ and $y$ .

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

Add $y z$ and $y z$ .

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

Step 7

Move $2 y z$ .

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

Step 8

Move $y^{2}$ .

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