Simplify (a+3)^2-a(a+3)

${(a + 3)}^{2} - a (a + 3)$

Step 1

Simplify each term.

Rewrite ${(a + 3)}^{2}$ as $(a + 3) (a + 3)$ .

$(a + 3) (a + 3) - a (a + 3)$

Expand $(a + 3) (a + 3)$ using the FOIL Method.

Apply the distributive property.

$a (a + 3) + 3 (a + 3) - a (a + 3)$

Apply the distributive property.

$a \cdot a + a \cdot 3 + 3 (a + 3) - a (a + 3)$

Apply the distributive property.

$a \cdot a + a \cdot 3 + 3 a + 3 \cdot 3 - a (a + 3)$

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

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

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

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

Multiply $3$ by $3$ .

$a^{2} + 3 a + 3 a + 9 - a (a + 3)$

Add $3 a$ and $3 a$ .

$a^{2} + 6 a + 9 - a (a + 3)$

Apply the distributive property.

$a^{2} + 6 a + 9 - a \cdot a - a \cdot 3$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$a^{2} + 6 a + 9 - (a \cdot a) - a \cdot 3$

Multiply $a$ by $a$ .

$a^{2} + 6 a + 9 - a^{2} - a \cdot 3$

Multiply $3$ by $- 1$ .

$a^{2} + 6 a + 9 - a^{2} - 3 a$

Step 2

Simplify by adding terms.

Combine the opposite terms in $a^{2} + 6 a + 9 - a^{2} - 3 a$ .

Subtract $a^{2}$ from $a^{2}$ .

$6 a + 9 + 0 - 3 a$

Add $6 a + 9$ and $0$ .

$6 a + 9 - 3 a$

Subtract $3 a$ from $6 a$ .

$3 a + 9$