Find the Product (3x-6)(2x^2-7x+1)

$(3 x - 6) (2 x^{2} - 7 x + 1)$

Expand $(3 x - 6) (2 x^{2} - 7 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $- 7$ .

$6 x^{3} - 21 x^{2} + 3 x \cdot 1 - 6 (2 x^{2}) - 6 (- 7 x) - 6 \cdot 1$

Multiply $3$ by $1$ .

$6 x^{3} - 21 x^{2} + 3 x - 6 (2 x^{2}) - 6 (- 7 x) - 6 \cdot 1$

Multiply $2$ by $- 6$ .

$6 x^{3} - 21 x^{2} + 3 x - 12 x^{2} - 6 (- 7 x) - 6 \cdot 1$

Multiply $- 7$ by $- 6$ .

$6 x^{3} - 21 x^{2} + 3 x - 12 x^{2} + 42 x - 6 \cdot 1$

Multiply $- 6$ by $1$ .

$6 x^{3} - 21 x^{2} + 3 x - 12 x^{2} + 42 x - 6$

Simplify by adding terms.

Subtract $12 x^{2}$ from $- 21 x^{2}$ .

$6 x^{3} - 33 x^{2} + 3 x + 42 x - 6$

Add $3 x$ and $42 x$ .

$6 x^{3} - 33 x^{2} + 45 x - 6$