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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

$a^{2} - 2 a b + b a - 2 b \cdot b$

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

Move $b$ .

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

Multiply $b$ by $b$ .

$a^{2} - 2 a b + b a - 2 b^{2}$

Add $- 2 a b$ and $b a$ .

Reorder $b$ and $a$ .

$a^{2} - 2 a b + a b - 2 b^{2}$

Add $- 2 a b$ and $a b$ .

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