Find the Perfect Square Trinomial (2q-4)^2

${(2 q - 4)}^{2}$

Step 1

Rewrite ${(2 q - 4)}^{2}$ as $(2 q - 4) (2 q - 4)$ .

$(2 q - 4) (2 q - 4)$

Step 2

Expand $(2 q - 4) (2 q - 4)$ using the FOIL Method.

Apply the distributive property.

$2 q (2 q - 4) - 4 (2 q - 4)$

Apply the distributive property.

$2 q (2 q) + 2 q \cdot - 4 - 4 (2 q - 4)$

Apply the distributive property.

$2 q (2 q) + 2 q \cdot - 4 - 4 (2 q) - 4 \cdot - 4$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 q \cdot q + 2 q \cdot - 4 - 4 (2 q) - 4 \cdot - 4$

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

$2 \cdot 2 (q \cdot q) + 2 q \cdot - 4 - 4 (2 q) - 4 \cdot - 4$

Multiply $q$ by $q$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 4$ by $2$ .

$4 q^{2} - 8 q - 4 (2 q) - 4 \cdot - 4$

Multiply $2$ by $- 4$ .

$4 q^{2} - 8 q - 8 q - 4 \cdot - 4$

Multiply $- 4$ by $- 4$ .

$4 q^{2} - 8 q - 8 q + 16$

Subtract $8 q$ from $- 8 q$ .

$4 q^{2} - 16 q + 16$