Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Multiply $a$ by $a$ .

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

Step 1.2.2

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

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

Step 1.2.3

Multiply $2$ by $- 1$ .

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

Tap for more steps...

Step 1.4.1

Apply the distributive property.

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

Step 1.4.2

Apply the distributive property.

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

Step 1.4.3

Apply the distributive property.

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

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

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

Tap for more steps...

Step 1.5.1.1

Move $a$ .

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

Step 1.5.1.2

Multiply $a$ by $a$ .

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

Step 1.5.2

Multiply $- 2$ by $- 1$ .

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

Step 1.5.3

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.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

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

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

Step 2.2

Add $2 a$ and $2 a$ .

$4 a - b a - b a$

Step 2.3

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

$4 a - 2 b a$