Find the Product (9-a)^2

${(9 - a)}^{2}$

Rewrite ${(9 - a)}^{2}$ as $(9 - a) (9 - a)$ .

$(9 - a) (9 - a)$

Expand $(9 - a) (9 - a)$ using the FOIL Method.

Apply the distributive property.

$9 (9 - a) - a (9 - a)$

Apply the distributive property.

$9 \cdot 9 + 9 (- a) - a (9 - a)$

Apply the distributive property.

$9 \cdot 9 + 9 (- a) - a \cdot 9 - a (- a)$

$9 \cdot 9 + 9 (- a) - a \cdot 9 - a (- a)$

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 (- a) - a \cdot 9 - a (- a)$

Multiply $- 1$ by $9$ .

$81 - 9 a - a \cdot 9 - a (- a)$

Multiply $9$ by $- 1$ .

$81 - 9 a - 9 a - a (- a)$

Rewrite using the commutative property of multiplication.

$81 - 9 a - 9 a - 1 \cdot - 1 a \cdot a$

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

Move $a$ .

$81 - 9 a - 9 a - 1 \cdot - 1 (a \cdot a)$

Multiply $a$ by $a$ .

$81 - 9 a - 9 a - 1 \cdot - 1 a^{2}$

$81 - 9 a - 9 a - 1 \cdot - 1 a^{2}$

Multiply $- 1$ by $- 1$ .

$81 - 9 a - 9 a + 1 a^{2}$

Multiply $a^{2}$ by $1$ .

$81 - 9 a - 9 a + a^{2}$

$81 - 9 a - 9 a + a^{2}$

Subtract $9 a$ from $- 9 a$ .

$81 - 18 a + a^{2}$

$81 - 18 a + a^{2}$

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