Find the Product (2x+6)^2

${(2 x + 6)}^{2}$

Step 1

Rewrite ${(2 x + 6)}^{2}$ as $(2 x + 6) (2 x + 6)$ .

$(2 x + 6) (2 x + 6)$

Step 2

Expand $(2 x + 6) (2 x + 6)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x + 6) + 6 (2 x + 6)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 6 + 6 (2 x + 6)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 6 + 6 (2 x) + 6 \cdot 6$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot 6 + 6 (2 x) + 6 \cdot 6$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot 6 + 6 (2 x) + 6 \cdot 6$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $6$ by $2$ .

$4 x^{2} + 12 x + 6 (2 x) + 6 \cdot 6$

Multiply $2$ by $6$ .

$4 x^{2} + 12 x + 12 x + 6 \cdot 6$

Multiply $6$ by $6$ .

$4 x^{2} + 12 x + 12 x + 36$

Add $12 x$ and $12 x$ .

$4 x^{2} + 24 x + 36$