Write in Standard Form (3x^2-2x+2)(-2x^2-3x-1)

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

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

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

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $3$ by $- 2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $3$ by $- 3$ .

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

Multiply $- 1$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 2$ by $- 2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $- 3$ .

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

Multiply $- 1$ by $- 2$ .

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

Multiply $- 2$ by $2$ .

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

Multiply $- 3$ by $2$ .

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

Multiply $2$ by $- 1$ .

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

Simplify by adding terms.

Add $- 9 x^{3}$ and $4 x^{3}$ .

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

Add $- 3 x^{2}$ and $6 x^{2}$ .

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

Subtract $4 x^{2}$ from $3 x^{2}$ .

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

Subtract $6 x$ from $2 x$ .

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

Write in Standard Form (3x^2-2x+2)(-2x^2-3x-1)

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