Find the Product 3(a-2)^2-(2-a)

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

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

Move $- 2$ to the left of $a$ .

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

Multiply $- 2$ by $- 2$ .

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

Subtract $2 a$ from $- 2 a$ .

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

Apply the distributive property.

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

Simplify.

Multiply $- 4$ by $3$ .

$3 a^{2} - 12 a + 3 \cdot 4 - (2 - a)$

Multiply $3$ by $4$ .

$3 a^{2} - 12 a + 12 - (2 - a)$

Apply the distributive property.

$3 a^{2} - 12 a + 12 - 1 \cdot 2 - - a$

Multiply $- 1$ by $2$ .

$3 a^{2} - 12 a + 12 - 2 - - a$

Multiply $- - a$ .

Multiply $- 1$ by $- 1$ .

$3 a^{2} - 12 a + 12 - 2 + 1 a$

Multiply $a$ by $1$ .

$3 a^{2} - 12 a + 12 - 2 + a$

Simplify by adding terms.

Add $- 12 a$ and $a$ .

$3 a^{2} - 11 a + 12 - 2$

Subtract $2$ from $12$ .

$3 a^{2} - 11 a + 10$