Simplify (2-3x)(3x^2-2x-1)

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Multiply $3$ by $2$ .

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

Multiply $- 2$ by $2$ .

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

Multiply $2$ by $- 1$ .

$6 x^{2} - 4 x - 2 - 3 x (3 x^{2}) - 3 x (- 2 x) - 3 x \cdot - 1$

Rewrite using the commutative property of multiplication.

$6 x^{2} - 4 x - 2 - 3 \cdot 3 x \cdot x^{2} - 3 x (- 2 x) - 3 x \cdot - 1$

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

Move $x^{2}$ .

$6 x^{2} - 4 x - 2 - 3 \cdot 3 (x^{2} x) - 3 x (- 2 x) - 3 x \cdot - 1$

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

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

$6 x^{2} - 4 x - 2 - 3 \cdot 3 (x^{2} x^{1}) - 3 x (- 2 x) - 3 x \cdot - 1$

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

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

Add $2$ and $1$ .

$6 x^{2} - 4 x - 2 - 3 \cdot 3 x^{3} - 3 x (- 2 x) - 3 x \cdot - 1$

Multiply $- 3$ by $3$ .

$6 x^{2} - 4 x - 2 - 9 x^{3} - 3 x (- 2 x) - 3 x \cdot - 1$

Rewrite using the commutative property of multiplication.

$6 x^{2} - 4 x - 2 - 9 x^{3} - 3 \cdot - 2 x \cdot x - 3 x \cdot - 1$

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

Move $x$ .

$6 x^{2} - 4 x - 2 - 9 x^{3} - 3 \cdot - 2 (x \cdot x) - 3 x \cdot - 1$

Multiply $x$ by $x$ .

$6 x^{2} - 4 x - 2 - 9 x^{3} - 3 \cdot - 2 x^{2} - 3 x \cdot - 1$

Multiply $- 3$ by $- 2$ .

$6 x^{2} - 4 x - 2 - 9 x^{3} + 6 x^{2} - 3 x \cdot - 1$

Multiply $- 1$ by $- 3$ .

$6 x^{2} - 4 x - 2 - 9 x^{3} + 6 x^{2} + 3 x$

Simplify by adding terms.

Add $6 x^{2}$ and $6 x^{2}$ .

$12 x^{2} - 4 x - 2 - 9 x^{3} + 3 x$

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

$12 x^{2} - x - 2 - 9 x^{3}$

Simplify the expression.

Move $- 2$ .

$12 x^{2} - x - 9 x^{3} - 2$

Move $- x$ .

$12 x^{2} - 9 x^{3} - x - 2$

Reorder $12 x^{2}$ and $- 9 x^{3}$ .

$- 9 x^{3} + 12 x^{2} - x - 2$

Simplify (2-3x)(3x^2-2x-1)

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