Find the Product (3a-5b)^2

${(3 a - 5 b)}^{2}$

Rewrite ${(3 a - 5 b)}^{2}$ as $(3 a - 5 b) (3 a - 5 b)$ .

$(3 a - 5 b) (3 a - 5 b)$

Expand $(3 a - 5 b) (3 a - 5 b)$ using the FOIL Method.

Apply the distributive property.

$3 a (3 a - 5 b) - 5 b (3 a - 5 b)$

Apply the distributive property.

$3 a (3 a) + 3 a (- 5 b) - 5 b (3 a - 5 b)$

Apply the distributive property.

$3 a (3 a) + 3 a (- 5 b) - 5 b (3 a) - 5 b (- 5 b)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 a \cdot a + 3 a (- 5 b) - 5 b (3 a) - 5 b (- 5 b)$

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

Move $a$ .

$3 \cdot 3 (a \cdot a) + 3 a (- 5 b) - 5 b (3 a) - 5 b (- 5 b)$

Multiply $a$ by $a$ .

$3 \cdot 3 a^{2} + 3 a (- 5 b) - 5 b (3 a) - 5 b (- 5 b)$

Multiply $3$ by $3$ .

$9 a^{2} + 3 a (- 5 b) - 5 b (3 a) - 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

$9 a^{2} + 3 \cdot - 5 a b - 5 b (3 a) - 5 b (- 5 b)$

Multiply $3$ by $- 5$ .

$9 a^{2} - 15 a b - 5 b (3 a) - 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

$9 a^{2} - 15 a b - 5 \cdot 3 b a - 5 b (- 5 b)$

Multiply $- 5$ by $3$ .

$9 a^{2} - 15 a b - 15 b a - 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

$9 a^{2} - 15 a b - 15 b a - 5 \cdot - 5 b \cdot b$

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

Move $b$ .

$9 a^{2} - 15 a b - 15 b a - 5 \cdot - 5 (b \cdot b)$

Multiply $b$ by $b$ .

$9 a^{2} - 15 a b - 15 b a - 5 \cdot - 5 b^{2}$

Multiply $- 5$ by $- 5$ .

$9 a^{2} - 15 a b - 15 b a + 25 b^{2}$

Subtract $15 b a$ from $- 15 a b$ .

Move $b$ .

$9 a^{2} - 15 a b - 15 a b + 25 b^{2}$

Subtract $15 a b$ from $- 15 a b$ .

$9 a^{2} - 30 a b + 25 b^{2}$