Find the Product (ab+3)^2

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

Step 1

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

$(a b + 3) (a b + 3)$

Step 2

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

Apply the distributive property.

$a b (a b + 3) + 3 (a b + 3)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

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

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

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

Multiply $3$ by $3$ .

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

Add $3 a b$ and $3 a b$ .

$a^{2} b^{2} + 6 a b + 9$