Write in Standard Form (-3x-1)(3x^2-9x+4)

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

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

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

Expand $(- 3 x - 1) (3 x^{2} - 9 x + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $- 9$ .

$- 9 x^{3} + 27 x^{2} - 3 x \cdot 4 - 1 (3 x^{2}) - 1 (- 9 x) - 1 \cdot 4$

Multiply $4$ by $- 3$ .

$- 9 x^{3} + 27 x^{2} - 12 x - 1 (3 x^{2}) - 1 (- 9 x) - 1 \cdot 4$

Multiply $3$ by $- 1$ .

$- 9 x^{3} + 27 x^{2} - 12 x - 3 x^{2} - 1 (- 9 x) - 1 \cdot 4$

Multiply $- 9$ by $- 1$ .

$- 9 x^{3} + 27 x^{2} - 12 x - 3 x^{2} + 9 x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$- 9 x^{3} + 27 x^{2} - 12 x - 3 x^{2} + 9 x - 4$

Simplify by adding terms.

Subtract $3 x^{2}$ from $27 x^{2}$ .

$- 9 x^{3} + 24 x^{2} - 12 x + 9 x - 4$

Add $- 12 x$ and $9 x$ .

$- 9 x^{3} + 24 x^{2} - 3 x - 4$