Simplify (a-b)(a+2)-(a+b)(a-2)

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

Step 1

Simplify each term.

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

Multiply $a$ by $a$ .

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

Move $2$ to the left of $a$ .

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

Multiply $2$ by $- 1$ .

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

Apply the distributive property.

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $- 2$ by $- 1$ .

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

Multiply $- 2$ by $- 1$ .

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

Step 2

Simplify by adding terms.

Combine the opposite terms in $a^{2} + 2 a - b a - 2 b - a^{2} + 2 a - b a + 2 b$ .

Subtract $a^{2}$ from $a^{2}$ .

$2 a - b a - 2 b + 0 + 2 a - b a + 2 b$

Add $2 a - b a - 2 b$ and $0$ .

$2 a - b a - 2 b + 2 a - b a + 2 b$

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

$2 a - b a + 2 a - b a + 0$

Add $2 a - b a + 2 a - b a$ and $0$ .

$2 a - b a + 2 a - b a$

Add $2 a$ and $2 a$ .

$4 a - b a - b a$

Subtract $b a$ from $- b a$ .

$4 a - 2 b a$

Simplify (a-b)(a+2)-(a+b)(a-2)

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