Simplify (2x-6)^2

${(2 x - 6)}^{2}$

Step 1

Rewrite ${(2 x - 6)}^{2}$ as $(2 x - 6) (2 x - 6)$ .

$(2 x - 6) (2 x - 6)$

Step 2

Expand $(2 x - 6) (2 x - 6)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 6) - 6 (2 x - 6)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 6 - 6 (2 x - 6)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

Multiply $- 6$ by $2$ .

$4 x^{2} - 12 x - 6 (2 x) - 6 \cdot - 6$

Multiply $2$ by $- 6$ .

$4 x^{2} - 12 x - 12 x - 6 \cdot - 6$

Multiply $- 6$ by $- 6$ .

$4 x^{2} - 12 x - 12 x + 36$

Subtract $12 x$ from $- 12 x$ .

$4 x^{2} - 24 x + 36$