Find the Product (7x-8)(3x+5y)

$(7 x - 8) (3 x + 5 y)$

Expand $(7 x - 8) (3 x + 5 y)$ using the FOIL Method.

Apply the distributive property.

$7 x (3 x + 5 y) - 8 (3 x + 5 y)$

Apply the distributive property.

$7 x (3 x) + 7 x (5 y) - 8 (3 x + 5 y)$

Apply the distributive property.

$7 x (3 x) + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 3 x \cdot x + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$7 \cdot 3 (x \cdot x) + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Multiply $x$ by $x$ .

$7 \cdot 3 x^{2} + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Multiply $7$ by $3$ .

$21 x^{2} + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Rewrite using the commutative property of multiplication.

$21 x^{2} + 7 \cdot 5 x y - 8 (3 x) - 8 (5 y)$

Multiply $7$ by $5$ .

$21 x^{2} + 35 x y - 8 (3 x) - 8 (5 y)$

Multiply $3$ by $- 8$ .

$21 x^{2} + 35 x y - 24 x - 8 (5 y)$

Multiply $5$ by $- 8$ .

$21 x^{2} + 35 x y - 24 x - 40 y$