Find the Product (2b-3c)(3c+2b)

$(2 b - 3 c) (3 c + 2 b)$

Step 1

Expand $(2 b - 3 c) (3 c + 2 b)$ using the FOIL Method.

Apply the distributive property.

$2 b (3 c + 2 b) - 3 c (3 c + 2 b)$

Apply the distributive property.

$2 b (3 c) + 2 b (2 b) - 3 c (3 c + 2 b)$

Apply the distributive property.

$2 b (3 c) + 2 b (2 b) - 3 c (3 c) - 3 c (2 b)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 b c + 2 b (2 b) - 3 c (3 c) - 3 c (2 b)$

Multiply $2$ by $3$ .

$6 b c + 2 b (2 b) - 3 c (3 c) - 3 c (2 b)$

Rewrite using the commutative property of multiplication.

$6 b c + 2 \cdot 2 b \cdot b - 3 c (3 c) - 3 c (2 b)$

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

Move $b$ .

$6 b c + 2 \cdot 2 (b \cdot b) - 3 c (3 c) - 3 c (2 b)$

Multiply $b$ by $b$ .

$6 b c + 2 \cdot 2 b^{2} - 3 c (3 c) - 3 c (2 b)$

Multiply $2$ by $2$ .

$6 b c + 4 b^{2} - 3 c (3 c) - 3 c (2 b)$

Rewrite using the commutative property of multiplication.

$6 b c + 4 b^{2} - 3 \cdot 3 c \cdot c - 3 c (2 b)$

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$6 b c + 4 b^{2} - 3 \cdot 3 (c \cdot c) - 3 c (2 b)$

Multiply $c$ by $c$ .

$6 b c + 4 b^{2} - 3 \cdot 3 c^{2} - 3 c (2 b)$

Multiply $- 3$ by $3$ .

$6 b c + 4 b^{2} - 9 c^{2} - 3 c (2 b)$

Rewrite using the commutative property of multiplication.

$6 b c + 4 b^{2} - 9 c^{2} - 3 \cdot 2 c b$

Multiply $- 3$ by $2$ .

$6 b c + 4 b^{2} - 9 c^{2} - 6 c b$

Subtract $6 c b$ from $6 b c$ .

Move $c$ .

$4 b^{2} - 9 c^{2} + 6 b c - 6 b c$

Subtract $6 b c$ from $6 b c$ .

$4 b^{2} - 9 c^{2} + 0$

Add $4 b^{2}$ and $0$ .

$4 b^{2} - 9 c^{2}$