Simplify -2xyz(xy+3yz)

$- 2 x y z (x y + 3 y z)$

Step 1

Apply the distributive property.

$- 2 x y z (x y) - 2 x y z (3 y z)$

Step 2

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 2 (x \cdot x) y z y - 2 x y z (3 y z)$

Multiply $x$ by $x$ .

$- 2 x^{2} y z y - 2 x y z (3 y z)$

$- 2 x^{2} y z y - 2 x y z (3 y z)$

Step 3

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$- 2 x^{2} y z y - 2 x (y \cdot y) z (3 z)$

Multiply $y$ by $y$ .

$- 2 x^{2} y z y - 2 x y^{2} z (3 z)$

$- 2 x^{2} y z y - 2 x y^{2} z (3 z)$

Step 4

Simplify each term.

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$- 2 x^{2} (y \cdot y) z - 2 x y^{2} z (3 z)$

Multiply $y$ by $y$ .

$- 2 x^{2} y^{2} z - 2 x y^{2} z (3 z)$

$- 2 x^{2} y^{2} z - 2 x y^{2} z (3 z)$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$- 2 x^{2} y^{2} z - 2 x y^{2} (z \cdot z) \cdot 3$

Multiply $z$ by $z$ .

$- 2 x^{2} y^{2} z - 2 x y^{2} z^{2} \cdot 3$

$- 2 x^{2} y^{2} z - 2 x y^{2} z^{2} \cdot 3$

Multiply $3$ by $- 2$ .

$- 2 x^{2} y^{2} z - 6 x y^{2} z^{2}$

$- 2 x^{2} y^{2} z - 6 x y^{2} z^{2}$

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