Simplify (x+2)(x^2+2x+3)

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $3$ to the left of $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $3$ .

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

Simplify by adding terms.

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

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

Add $3 x$ and $4 x$ .

$x^{3} + 4 x^{2} + 7 x + 6$