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

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

Simplify each term.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $2$ .

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

Multiply $3$ by $- 2$ .

$2 x^{3} + 2 x^{2} - 4 x + 3 x^{2} + 3 x - 6$

Simplify by adding terms.

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

$2 x^{3} + 5 x^{2} - 4 x + 3 x - 6$

Add $- 4 x$ and $3 x$ .

$2 x^{3} + 5 x^{2} - x - 6$