Simplify (2x+3)^2

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

Step 1

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

$(2 x + 3) (2 x + 3)$

Step 2

Expand $(2 x + 3) (2 x + 3)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x + 3) + 3 (2 x + 3)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 3 + 3 (2 x + 3)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot 3 + 3 (2 x) + 3 \cdot 3$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $3$ by $2$ .

$4 x^{2} + 6 x + 3 (2 x) + 3 \cdot 3$

Multiply $2$ by $3$ .

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

Multiply $3$ by $3$ .

$4 x^{2} + 6 x + 6 x + 9$

Add $6 x$ and $6 x$ .

$4 x^{2} + 12 x + 9$