Write in Standard Form 3m(3m+6)-3(m^2+4m+1)

$3 m (3 m + 6) - 3 (m^{2} + 4 m + 1)$

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

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

Simplify each term.

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Multiply $6$ by $3$ .

$3 \cdot 3 m \cdot m + 18 m - 3 (m^{2} + 4 m + 1)$

Simplify each term.

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$3 \cdot 3 (m \cdot m) + 18 m - 3 (m^{2} + 4 m + 1)$

Multiply $m$ by $m$ .

$3 \cdot 3 m^{2} + 18 m - 3 (m^{2} + 4 m + 1)$

Multiply $3$ by $3$ .

$9 m^{2} + 18 m - 3 (m^{2} + 4 m + 1)$

Apply the distributive property.

$9 m^{2} + 18 m - 3 m^{2} - 3 (4 m) - 3 \cdot 1$

Simplify.

Multiply $4$ by $- 3$ .

$9 m^{2} + 18 m - 3 m^{2} - 12 m - 3 \cdot 1$

Multiply $- 3$ by $1$ .

$9 m^{2} + 18 m - 3 m^{2} - 12 m - 3$

Simplify by adding terms.

Subtract $3 m^{2}$ from $9 m^{2}$ .

$6 m^{2} + 18 m - 12 m - 3$

Subtract $12 m$ from $18 m$ .

$6 m^{2} + 6 m - 3$