Find the Product (2a+5b)(a-4b)

$(2 a + 5 b) (a - 4 b)$

Expand $(2 a + 5 b) (a - 4 b)$ using the FOIL Method.

Apply the distributive property.

$2 a (a - 4 b) + 5 b (a - 4 b)$

Apply the distributive property.

$2 a \cdot a + 2 a (- 4 b) + 5 b (a - 4 b)$

Apply the distributive property.

$2 a \cdot a + 2 a (- 4 b) + 5 b a + 5 b (- 4 b)$

Simplify and combine like terms.

Simplify each term.

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

Move $a$ .

$2 (a \cdot a) + 2 a (- 4 b) + 5 b a + 5 b (- 4 b)$

Multiply $a$ by $a$ .

$2 a^{2} + 2 a (- 4 b) + 5 b a + 5 b (- 4 b)$

Rewrite using the commutative property of multiplication.

$2 a^{2} + 2 \cdot - 4 a b + 5 b a + 5 b (- 4 b)$

Multiply $2$ by $- 4$ .

$2 a^{2} - 8 a b + 5 b a + 5 b (- 4 b)$

Rewrite using the commutative property of multiplication.

$2 a^{2} - 8 a b + 5 b a + 5 \cdot - 4 b \cdot b$

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

Move $b$ .

$2 a^{2} - 8 a b + 5 b a + 5 \cdot - 4 (b \cdot b)$

Multiply $b$ by $b$ .

$2 a^{2} - 8 a b + 5 b a + 5 \cdot - 4 b^{2}$

Multiply $5$ by $- 4$ .

$2 a^{2} - 8 a b + 5 b a - 20 b^{2}$

Add $- 8 a b$ and $5 b a$ .

Move $b$ .

$2 a^{2} - 8 a b + 5 a b - 20 b^{2}$

Add $- 8 a b$ and $5 a b$ .

$2 a^{2} - 3 a b - 20 b^{2}$