Simplify 3(a+1)+(a+4)(2+a)

$3 (a + 1) + (a + 4) (2 + a)$

Simplify each term.

Apply the distributive property.

$3 a + 3 \cdot 1 + (a + 4) (2 + a)$

Multiply $3$ by $1$ .

$3 a + 3 + (a + 4) (2 + a)$

Expand $(a + 4) (2 + a)$ using the FOIL Method.

Apply the distributive property.

$3 a + 3 + a (2 + a) + 4 (2 + a)$

Apply the distributive property.

$3 a + 3 + a \cdot 2 + a \cdot a + 4 (2 + a)$

Apply the distributive property.

$3 a + 3 + a \cdot 2 + a \cdot a + 4 \cdot 2 + 4 a$

Simplify and combine like terms.

Simplify each term.

Move $2$ to the left of $a$ .

$3 a + 3 + 2 \cdot a + a \cdot a + 4 \cdot 2 + 4 a$

Multiply $a$ by $a$ .

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

Multiply $4$ by $2$ .

$3 a + 3 + 2 a + a^{2} + 8 + 4 a$

Add $2 a$ and $4 a$ .

$3 a + 3 + 6 a + a^{2} + 8$

Simplify by adding terms.

Add $3 a$ and $6 a$ .

$9 a + 3 + a^{2} + 8$

Simplify the expression.

Add $3$ and $8$ .

$9 a + a^{2} + 11$

Reorder $9 a$ and $a^{2}$ .

$a^{2} + 9 a + 11$