Write in Standard Form (2x+3)(3x^2-6x+2)

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

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

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

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

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 6$ .

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

Multiply $2$ by $2$ .

$6 x^{3} - 12 x^{2} + 4 x + 3 (3 x^{2}) + 3 (- 6 x) + 3 \cdot 2$

Multiply $3$ by $3$ .

$6 x^{3} - 12 x^{2} + 4 x + 9 x^{2} + 3 (- 6 x) + 3 \cdot 2$

Multiply $- 6$ by $3$ .

$6 x^{3} - 12 x^{2} + 4 x + 9 x^{2} - 18 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$6 x^{3} - 12 x^{2} + 4 x + 9 x^{2} - 18 x + 6$

Simplify by adding terms.

Add $- 12 x^{2}$ and $9 x^{2}$ .

$6 x^{3} - 3 x^{2} + 4 x - 18 x + 6$

Subtract $18 x$ from $4 x$ .

$6 x^{3} - 3 x^{2} - 14 x + 6$