Simplify 3x(2x^2-4x+2)-(5x^2-7x-8)

$3 x (2 x^{2} - 4 x + 2) - (5 x^{2} - 7 x - 8)$

Simplify each term.

Apply the distributive property.

$3 x (2 x^{2}) + 3 x (- 4 x) + 3 x \cdot 2 - (5 x^{2} - 7 x - 8)$

Simplify.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x^{2} + 3 x (- 4 x) + 3 x \cdot 2 - (5 x^{2} - 7 x - 8)$

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x^{2} + 3 \cdot - 4 x \cdot x + 3 x \cdot 2 - (5 x^{2} - 7 x - 8)$

Multiply $2$ by $3$ .

$3 \cdot 2 x \cdot x^{2} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Simplify each term.

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

Move $x^{2}$ .

$3 \cdot 2 (x^{2} x) + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

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

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

$3 \cdot 2 (x^{2} x^{1}) + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

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

$3 \cdot 2 x^{2 + 1} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Add $2$ and $1$ .

$3 \cdot 2 x^{3} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

Multiply $3$ by $2$ .

$6 x^{3} + 3 \cdot - 4 x \cdot x + 6 x - (5 x^{2} - 7 x - 8)$

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

Move $x$ .

$6 x^{3} + 3 \cdot - 4 (x \cdot x) + 6 x - (5 x^{2} - 7 x - 8)$

Multiply $x$ by $x$ .

$6 x^{3} + 3 \cdot - 4 x^{2} + 6 x - (5 x^{2} - 7 x - 8)$

Multiply $3$ by $- 4$ .

$6 x^{3} - 12 x^{2} + 6 x - (5 x^{2} - 7 x - 8)$

Apply the distributive property.

$6 x^{3} - 12 x^{2} + 6 x - (5 x^{2}) - (- 7 x) - - 8$

Simplify.

Multiply $5$ by $- 1$ .

$6 x^{3} - 12 x^{2} + 6 x - 5 x^{2} - (- 7 x) - - 8$

Multiply $- 7$ by $- 1$ .

$6 x^{3} - 12 x^{2} + 6 x - 5 x^{2} + 7 x - - 8$

Multiply $- 1$ by $- 8$ .

$6 x^{3} - 12 x^{2} + 6 x - 5 x^{2} + 7 x + 8$

Simplify by adding terms.

Subtract $5 x^{2}$ from $- 12 x^{2}$ .

$6 x^{3} - 17 x^{2} + 6 x + 7 x + 8$

Add $6 x$ and $7 x$ .

$6 x^{3} - 17 x^{2} + 13 x + 8$