Find the Product (2x^2-x+1)(x-3)

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

Expand $(2 x^{2} - x + 1) (x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$2 x^{2} x + 2 x^{2} \cdot - 3 - x \cdot x - x \cdot - 3 + 1 x + 1 \cdot - 3$

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

$2 x^{1 + 2} + 2 x^{2} \cdot - 3 - x \cdot x - x \cdot - 3 + 1 x + 1 \cdot - 3$

Add $1$ and $2$ .

$2 x^{3} + 2 x^{2} \cdot - 3 - x \cdot x - x \cdot - 3 + 1 x + 1 \cdot - 3$

Multiply $- 3$ by $2$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 3$ by $1$ .

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

Simplify by adding terms.

Subtract $x^{2}$ from $- 6 x^{2}$ .

$2 x^{3} - 7 x^{2} + 3 x + x - 3$

Add $3 x$ and $x$ .

$2 x^{3} - 7 x^{2} + 4 x - 3$