Simplify 3(x+2)(x^2-x-8)

$3 (x + 2) (x^{2} - x - 8)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$(3 x + 3 \cdot 2) (x^{2} - x - 8)$

Multiply $3$ by $2$ .

$(3 x + 6) (x^{2} - x - 8)$

Step 2

Expand $(3 x + 6) (x^{2} - x - 8)$ by multiplying each term in the first expression by each term in the second expression.

$3 x \cdot x^{2} + 3 x (- x) + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

Step 3

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

$3 (x^{2} x) + 3 x (- x) + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

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

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

$3 (x^{2} x^{1}) + 3 x (- x) + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

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

$3 x^{2 + 1} + 3 x (- x) + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

Add $2$ and $1$ .

$3 x^{3} + 3 x (- x) + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

Rewrite using the commutative property of multiplication.

$3 x^{3} + 3 \cdot - 1 x \cdot x + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

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

Move $x$ .

$3 x^{3} + 3 \cdot - 1 (x \cdot x) + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

Multiply $x$ by $x$ .

$3 x^{3} + 3 \cdot - 1 x^{2} + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

Multiply $3$ by $- 1$ .

$3 x^{3} - 3 x^{2} + 3 x \cdot - 8 + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

Multiply $- 8$ by $3$ .

$3 x^{3} - 3 x^{2} - 24 x + 6 x^{2} + 6 (- x) + 6 \cdot - 8$

Multiply $- 1$ by $6$ .

$3 x^{3} - 3 x^{2} - 24 x + 6 x^{2} - 6 x + 6 \cdot - 8$

Multiply $6$ by $- 8$ .

$3 x^{3} - 3 x^{2} - 24 x + 6 x^{2} - 6 x - 48$

Simplify by adding terms.

Add $- 3 x^{2}$ and $6 x^{2}$ .

$3 x^{3} + 3 x^{2} - 24 x - 6 x - 48$

Subtract $6 x$ from $- 24 x$ .

$3 x^{3} + 3 x^{2} - 30 x - 48$