Expand the Trigonometric Expression (2a-3)^2

${(2 a - 3)}^{2}$

Step 1

Rewrite ${(2 a - 3)}^{2}$ as $(2 a - 3) (2 a - 3)$ .

$(2 a - 3) (2 a - 3)$

Step 2

Expand $(2 a - 3) (2 a - 3)$ using the FOIL Method.

Apply the distributive property.

$2 a (2 a - 3) - 3 (2 a - 3)$

Apply the distributive property.

$2 a (2 a) + 2 a \cdot - 3 - 3 (2 a - 3)$

Apply the distributive property.

$2 a (2 a) + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3$

Multiply $a$ by $a$ .

$2 \cdot 2 a^{2} + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3$

Multiply $2$ by $2$ .

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

Multiply $- 3$ by $2$ .

$4 a^{2} - 6 a - 3 (2 a) - 3 \cdot - 3$

Multiply $2$ by $- 3$ .

$4 a^{2} - 6 a - 6 a - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$4 a^{2} - 6 a - 6 a + 9$

Subtract $6 a$ from $- 6 a$ .

$4 a^{2} - 12 a + 9$