Find the Product (a-3b)^2

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

Rewrite ${(a - 3 b)}^{2}$ as $(a - 3 b) (a - 3 b)$ .

$(a - 3 b) (a - 3 b)$

Expand $(a - 3 b) (a - 3 b)$ using the FOIL Method.

Apply the distributive property.

$a (a - 3 b) - 3 b (a - 3 b)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

$a^{2} - 3 a b - 3 b a - 3 \cdot - 3 b \cdot b$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

$a^{2} - 3 a b - 3 b a - 3 \cdot - 3 b^{2}$

Multiply $- 3$ by $- 3$ .

$a^{2} - 3 a b - 3 b a + 9 b^{2}$

Subtract $3 b a$ from $- 3 a b$ .

Move $b$ .

$a^{2} - 3 a b - 3 a b + 9 b^{2}$

Subtract $3 a b$ from $- 3 a b$ .

$a^{2} - 6 a b + 9 b^{2}$