Expand the Trigonometric Expression 3(2x+1)^2

$3 {(2 x + 1)}^{2}$

Step 1

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

$3 ((2 x + 1) (2 x + 1))$

Step 2

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

Apply the distributive property.

$3 (2 x (2 x + 1) + 1 (2 x + 1))$

Apply the distributive property.

$3 (2 x (2 x) + 2 x \cdot 1 + 1 (2 x + 1))$

Apply the distributive property.

$3 (2 x (2 x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 (2 \cdot 2 x \cdot x + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1)$

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

Move $x$ .

$3 (2 \cdot 2 (x \cdot x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1)$

Multiply $x$ by $x$ .

$3 (2 \cdot 2 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1)$

Multiply $2$ by $2$ .

$3 (4 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1)$

Multiply $2$ by $1$ .

$3 (4 x^{2} + 2 x + 1 (2 x) + 1 \cdot 1)$

Multiply $2 x$ by $1$ .

$3 (4 x^{2} + 2 x + 2 x + 1 \cdot 1)$

Multiply $1$ by $1$ .

$3 (4 x^{2} + 2 x + 2 x + 1)$

Add $2 x$ and $2 x$ .

$3 (4 x^{2} + 4 x + 1)$

Step 4

Apply the distributive property.

$3 (4 x^{2}) + 3 (4 x) + 3 \cdot 1$

Step 5

Simplify.

Multiply $4$ by $3$ .

$12 x^{2} + 3 (4 x) + 3 \cdot 1$

Multiply $4$ by $3$ .

$12 x^{2} + 12 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$12 x^{2} + 12 x + 3$