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

$(3 x + 4) (x^{2} + 2 x + 3)$

Step 1

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

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

Step 2

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

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

Step 3

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $2$ .

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

Multiply $3$ by $3$ .

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

Multiply $2$ by $4$ .

$3 x^{3} + 6 x^{2} + 9 x + 4 x^{2} + 8 x + 4 \cdot 3$

Multiply $4$ by $3$ .

$3 x^{3} + 6 x^{2} + 9 x + 4 x^{2} + 8 x + 12$

Simplify by adding terms.

Add $6 x^{2}$ and $4 x^{2}$ .

$3 x^{3} + 10 x^{2} + 9 x + 8 x + 12$

Add $9 x$ and $8 x$ .

$3 x^{3} + 10 x^{2} + 17 x + 12$