Simplify (2x+1)^2

${(2 x + 1)}^{2}$

Step 1

Rewrite ${(2 x + 1)}^{2}$ as $(2 x + 1) (2 x + 1)$ .

$(2 x + 1) (2 x + 1)$

Step 2

Expand $(2 x + 1) (2 x + 1)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x + 1) + 1 (2 x + 1)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 1 + 1 (2 x + 1)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Multiply $2$ by $1$ .

$4 x^{2} + 2 x + 1 (2 x) + 1 \cdot 1$

Multiply $2 x$ by $1$ .

$4 x^{2} + 2 x + 2 x + 1 \cdot 1$

Multiply $1$ by $1$ .

$4 x^{2} + 2 x + 2 x + 1$

Add $2 x$ and $2 x$ .

$4 x^{2} + 4 x + 1$