Find the Product (4ab+3c)(5ab+7c)

$(4 a b + 3 c) (5 a b + 7 c)$

Expand $(4 a b + 3 c) (5 a b + 7 c)$ using the FOIL Method.

Apply the distributive property.

$4 a b (5 a b + 7 c) + 3 c (5 a b + 7 c)$

Apply the distributive property.

$4 a b (5 a b) + 4 a b (7 c) + 3 c (5 a b + 7 c)$

Apply the distributive property.

$4 a b (5 a b) + 4 a b (7 c) + 3 c (5 a b) + 3 c (7 c)$

Simplify and combine like terms.

Simplify each term.

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

Move $a$ .

$4 (a \cdot a) b (5 b) + 4 a b (7 c) + 3 c (5 a b) + 3 c (7 c)$

Multiply $a$ by $a$ .

$4 a^{2} b (5 b) + 4 a b (7 c) + 3 c (5 a b) + 3 c (7 c)$

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

Move $b$ .

$4 a^{2} (b \cdot b) \cdot 5 + 4 a b (7 c) + 3 c (5 a b) + 3 c (7 c)$

Multiply $b$ by $b$ .

$4 a^{2} b^{2} \cdot 5 + 4 a b (7 c) + 3 c (5 a b) + 3 c (7 c)$

Multiply $5$ by $4$ .

$20 a^{2} b^{2} + 4 a b (7 c) + 3 c (5 a b) + 3 c (7 c)$

Multiply $7$ by $4$ .

$20 a^{2} b^{2} + 28 a b c + 3 c (5 a b) + 3 c (7 c)$

Multiply $5$ by $3$ .

$20 a^{2} b^{2} + 28 a b c + 15 c (a b) + 3 c (7 c)$

Rewrite using the commutative property of multiplication.

$20 a^{2} b^{2} + 28 a b c + 15 c a b + 3 \cdot 7 c \cdot c$

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

Move $c$ .

$20 a^{2} b^{2} + 28 a b c + 15 c a b + 3 \cdot 7 (c \cdot c)$

Multiply $c$ by $c$ .

$20 a^{2} b^{2} + 28 a b c + 15 c a b + 3 \cdot 7 c^{2}$

Multiply $3$ by $7$ .

$20 a^{2} b^{2} + 28 a b c + 15 c a b + 21 c^{2}$

Add $28 a b c$ and $15 c a b$ .

Move $c$ .

$20 a^{2} b^{2} + 28 a b c + 15 a b c + 21 c^{2}$

Add $28 a b c$ and $15 a b c$ .

$20 a^{2} b^{2} + 43 a b c + 21 c^{2}$