Expand the Trigonometric Expression (6x-6)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $6$ by $6$ .

$36 x^{2} + 6 x \cdot - 6 - 6 (6 x) - 6 \cdot - 6$

Multiply $- 6$ by $6$ .

$36 x^{2} - 36 x - 6 (6 x) - 6 \cdot - 6$

Multiply $6$ by $- 6$ .

$36 x^{2} - 36 x - 36 x - 6 \cdot - 6$

Multiply $- 6$ by $- 6$ .

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

Subtract $36 x$ from $- 36 x$ .

$36 x^{2} - 72 x + 36$