Expand the Trigonometric Expression (2+3d)(2+3d)

$(2 + 3 d) (2 + 3 d)$

Step 1

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

Apply the distributive property.

$2 (2 + 3 d) + 3 d (2 + 3 d)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (3 d) + 3 d \cdot 2 + 3 d (3 d)$

Multiply $3$ by $2$ .

$4 + 6 d + 3 d \cdot 2 + 3 d (3 d)$

Multiply $2$ by $3$ .

$4 + 6 d + 6 d + 3 d (3 d)$

Rewrite using the commutative property of multiplication.

$4 + 6 d + 6 d + 3 \cdot 3 d \cdot d$

Multiply $d$ by $d$ by adding the exponents.

Move $d$ .

$4 + 6 d + 6 d + 3 \cdot 3 (d \cdot d)$

Multiply $d$ by $d$ .

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

Multiply $3$ by $3$ .

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

Add $6 d$ and $6 d$ .

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