Find the Product (x-3)(2x^2-5x+1)

$(x - 3) (2 x^{2} - 5 x + 1)$

Step 1

Expand $(x - 3) (2 x^{2} - 5 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$x (2 x^{2}) + x (- 5 x) + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 x \cdot x^{2} + x (- 5 x) + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

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

Move $x^{2}$ .

$2 (x^{2} x) + x (- 5 x) + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

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

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

$2 (x^{2} x^{1}) + x (- 5 x) + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

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

$2 x^{2 + 1} + x (- 5 x) + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

Add $2$ and $1$ .

$2 x^{3} + x (- 5 x) + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

Rewrite using the commutative property of multiplication.

$2 x^{3} - 5 x \cdot x + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

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

Move $x$ .

$2 x^{3} - 5 (x \cdot x) + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

Multiply $x$ by $x$ .

$2 x^{3} - 5 x^{2} + x \cdot 1 - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

Multiply $x$ by $1$ .

$2 x^{3} - 5 x^{2} + x - 3 (2 x^{2}) - 3 (- 5 x) - 3 \cdot 1$

Multiply $2$ by $- 3$ .

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

Multiply $- 5$ by $- 3$ .

$2 x^{3} - 5 x^{2} + x - 6 x^{2} + 15 x - 3 \cdot 1$

Multiply $- 3$ by $1$ .

$2 x^{3} - 5 x^{2} + x - 6 x^{2} + 15 x - 3$

Simplify by adding terms.

Subtract $6 x^{2}$ from $- 5 x^{2}$ .

$2 x^{3} - 11 x^{2} + x + 15 x - 3$

Add $x$ and $15 x$ .

$2 x^{3} - 11 x^{2} + 16 x - 3$