Evaluate (4c-3d)(3c+d)

$(4 c - 3 d) (3 c + d)$

Step 1

Expand $(4 c - 3 d) (3 c + d)$ using the FOIL Method.

Apply the distributive property.

$4 c (3 c + d) - 3 d (3 c + d)$

Apply the distributive property.

$4 c (3 c) + 4 c d - 3 d (3 c + d)$

Apply the distributive property.

$4 c (3 c) + 4 c d - 3 d (3 c) - 3 d \cdot d$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 3 c \cdot c + 4 c d - 3 d (3 c) - 3 d \cdot d$

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

Move $c$ .

$4 \cdot 3 (c \cdot c) + 4 c d - 3 d (3 c) - 3 d \cdot d$

Multiply $c$ by $c$ .

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

Multiply $4$ by $3$ .

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

Rewrite using the commutative property of multiplication.

$12 c^{2} + 4 c d - 3 \cdot 3 d c - 3 d \cdot d$

Multiply $- 3$ by $3$ .

$12 c^{2} + 4 c d - 9 d c - 3 d \cdot d$

Multiply $d$ by $d$ by adding the exponents.

Move $d$ .

$12 c^{2} + 4 c d - 9 d c - 3 (d \cdot d)$

Multiply $d$ by $d$ .

$12 c^{2} + 4 c d - 9 d c - 3 d^{2}$

Subtract $9 d c$ from $4 c d$ .

Move $d$ .

$12 c^{2} + 4 c d - 9 c d - 3 d^{2}$

Subtract $9 c d$ from $4 c d$ .

$12 c^{2} - 5 c d - 3 d^{2}$