Simplify -9x(x^2+2x+4)

$- 9 x (x^{2} + 2 x + 4)$

Step 1

Apply the distributive property.

$- 9 x \cdot x^{2} - 9 x (2 x) - 9 x \cdot 4$

Step 2

Simplify.

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

Move $x^{2}$ .

$- 9 (x^{2} x) - 9 x (2 x) - 9 x \cdot 4$

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

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

$- 9 (x^{2} x^{1}) - 9 x (2 x) - 9 x \cdot 4$

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

$- 9 x^{2 + 1} - 9 x (2 x) - 9 x \cdot 4$

Add $2$ and $1$ .

$- 9 x^{3} - 9 x (2 x) - 9 x \cdot 4$

Rewrite using the commutative property of multiplication.

$- 9 x^{3} - 9 \cdot 2 x \cdot x - 9 x \cdot 4$

Multiply $4$ by $- 9$ .

$- 9 x^{3} - 9 \cdot 2 x \cdot x - 36 x$

Step 3

Simplify each term.

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

Move $x$ .

$- 9 x^{3} - 9 \cdot 2 (x \cdot x) - 36 x$

Multiply $x$ by $x$ .

$- 9 x^{3} - 9 \cdot 2 x^{2} - 36 x$

Multiply $- 9$ by $2$ .

$- 9 x^{3} - 18 x^{2} - 36 x$