Basic Math Examples

$(a + b) (a - b - c)$

Step 1

Expand $(a + b) (a - b - c)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $a \cdot a + a (- b) + a (- c) + b a + b (- b) + b (- c)$ .

Tap for more steps...

Step 2.1.1

Reorder the factors in the terms $a (- b)$ and $b a$ .

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

Step 2.1.2

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

$a \cdot a + a (- c) + 0 + b (- b) + b (- c)$

Step 2.1.3

Add $a \cdot a + a (- c)$ and $0$ .

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

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Multiply $a$ by $a$ .

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

Step 2.2.2

Rewrite using the commutative property of multiplication.

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

Step 2.2.3

Rewrite using the commutative property of multiplication.

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

Step 2.2.4

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

Tap for more steps...

Step 2.2.4.1

Move $b$ .

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

Step 2.2.4.2

Multiply $b$ by $b$ .

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

Step 2.2.5

Rewrite using the commutative property of multiplication.

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

Step 2.3

Reorder.

Tap for more steps...

Step 2.3.1

Move $- b^{2}$ .

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

Step 2.3.2

Move $a^{2}$ .

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