Find the Product (4ab-7c)(ab+6c)

$(4 a b - 7 c) (a b + 6 c)$

Expand $(4 a b - 7 c) (a b + 6 c)$ using the FOIL Method.

Apply the distributive property.

$4 a b (a b + 6 c) - 7 c (a b + 6 c)$

Apply the distributive property.

$4 a b (a b) + 4 a b (6 c) - 7 c (a b + 6 c)$

Apply the distributive property.

$4 a b (a b) + 4 a b (6 c) - 7 c (a b) - 7 c (6 c)$

Simplify and combine like terms.

Simplify each term.

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

Move $a$ .

$4 (a \cdot a) b \cdot b + 4 a b (6 c) - 7 c (a b) - 7 c (6 c)$

Multiply $a$ by $a$ .

$4 a^{2} b \cdot b + 4 a b (6 c) - 7 c (a b) - 7 c (6 c)$

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

Move $b$ .

$4 a^{2} (b \cdot b) + 4 a b (6 c) - 7 c (a b) - 7 c (6 c)$

Multiply $b$ by $b$ .

$4 a^{2} b^{2} + 4 a b (6 c) - 7 c (a b) - 7 c (6 c)$

Multiply $6$ by $4$ .

$4 a^{2} b^{2} + 24 a b c - 7 c (a b) - 7 c (6 c)$

Rewrite using the commutative property of multiplication.

$4 a^{2} b^{2} + 24 a b c - 7 c a b - 7 \cdot 6 c \cdot c$

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

Move $c$ .

$4 a^{2} b^{2} + 24 a b c - 7 c a b - 7 \cdot 6 (c \cdot c)$

Multiply $c$ by $c$ .

$4 a^{2} b^{2} + 24 a b c - 7 c a b - 7 \cdot 6 c^{2}$

Multiply $- 7$ by $6$ .

$4 a^{2} b^{2} + 24 a b c - 7 c a b - 42 c^{2}$

Subtract $7 c a b$ from $24 a b c$ .

Move $c$ .

$4 a^{2} b^{2} + 24 a b c - 7 a b c - 42 c^{2}$

Subtract $7 a b c$ from $24 a b c$ .

$4 a^{2} b^{2} + 17 a b c - 42 c^{2}$