Simplify -3x^2(6xy-2x^3y^2z)

$- 3 x^{2} (6 x y - 2 x^{3} y^{2} z)$

Step 1

Apply the distributive property.

$- 3 x^{2} (6 x y) - 3 x^{2} (- 2 x^{3} y^{2} z)$

Step 2

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$- 3 (x \cdot x^{2}) (6 y) - 3 x^{2} (- 2 x^{3} y^{2} z)$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$- 3 (x^{1} x^{2}) (6 y) - 3 x^{2} (- 2 x^{3} y^{2} z)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 3 x^{1 + 2} (6 y) - 3 x^{2} (- 2 x^{3} y^{2} z)$

Add $1$ and $2$ .

$- 3 x^{3} (6 y) - 3 x^{2} (- 2 x^{3} y^{2} z)$

Step 3

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$- 3 x^{3} (6 y) - 3 (x^{3} x^{2}) (- 2 y^{2} z)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 3 x^{3} (6 y) - 3 x^{3 + 2} (- 2 y^{2} z)$

Add $3$ and $2$ .

$- 3 x^{3} (6 y) - 3 x^{5} (- 2 y^{2} z)$

Step 4

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 3 \cdot 6 x^{3} y - 3 x^{5} (- 2 y^{2} z)$

Multiply $- 3$ by $6$ .

$- 18 x^{3} y - 3 x^{5} (- 2 y^{2} z)$

Multiply $- 2$ by $- 3$ .

$- 18 x^{3} y + 6 x^{5} y^{2} z$