Simplify 2(x+7)(x^2-3x-6)

$2 (x + 7) (x^{2} - 3 x - 6)$

Simplify by multiplying through.

Apply the distributive property.

$(2 x + 2 \cdot 7) (x^{2} - 3 x - 6)$

Multiply $2$ by $7$ .

$(2 x + 14) (x^{2} - 3 x - 6)$

Expand $(2 x + 14) (x^{2} - 3 x - 6)$ by multiplying each term in the first expression by each term in the second expression.

$2 x \cdot x^{2} + 2 x (- 3 x) + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

$2 (x^{2} x) + 2 x (- 3 x) + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

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

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

$2 (x^{2} x^{1}) + 2 x (- 3 x) + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

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

$2 x^{2 + 1} + 2 x (- 3 x) + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

Add $2$ and $1$ .

$2 x^{3} + 2 x (- 3 x) + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

Rewrite using the commutative property of multiplication.

$2 x^{3} + 2 \cdot - 3 x \cdot x + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

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

Move $x$ .

$2 x^{3} + 2 \cdot - 3 (x \cdot x) + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

Multiply $x$ by $x$ .

$2 x^{3} + 2 \cdot - 3 x^{2} + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

Multiply $2$ by $- 3$ .

$2 x^{3} - 6 x^{2} + 2 x \cdot - 6 + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

Multiply $- 6$ by $2$ .

$2 x^{3} - 6 x^{2} - 12 x + 14 x^{2} + 14 (- 3 x) + 14 \cdot - 6$

Multiply $- 3$ by $14$ .

$2 x^{3} - 6 x^{2} - 12 x + 14 x^{2} - 42 x + 14 \cdot - 6$

Multiply $14$ by $- 6$ .

$2 x^{3} - 6 x^{2} - 12 x + 14 x^{2} - 42 x - 84$

Simplify by adding terms.

Add $- 6 x^{2}$ and $14 x^{2}$ .

$2 x^{3} + 8 x^{2} - 12 x - 42 x - 84$

Subtract $42 x$ from $- 12 x$ .

$2 x^{3} + 8 x^{2} - 54 x - 84$