Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $a$ by $a$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

Multiply $b$ by $b$ .

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

Step 3.4

Rewrite using the commutative property of multiplication.

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

Step 3.5

Rewrite using the commutative property of multiplication.

$a^{2} + a b - a c + b a + b^{2} - b c - c a - c b - 1 \cdot - 1 c \cdot c$

Step 3.6

Multiply $c$ by $c$ by adding the exponents.

Tap for more steps...

Step 3.6.1

Move $c$ .

$a^{2} + a b - a c + b a + b^{2} - b c - c a - c b - 1 \cdot - 1 (c \cdot c)$

Step 3.6.2

Multiply $c$ by $c$ .

$a^{2} + a b - a c + b a + b^{2} - b c - c a - c b - 1 \cdot - 1 c^{2}$

Step 3.7

Multiply $- 1$ by $- 1$ .

$a^{2} + a b - a c + b a + b^{2} - b c - c a - c b + 1 c^{2}$

Step 3.8

Multiply $c^{2}$ by $1$ .

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

Step 4

Add $a b$ and $b a$ .

Tap for more steps...

Step 4.1

Reorder $b$ and $a$ .

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

Step 4.2

Add $a b$ and $a b$ .

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

Step 5

Subtract $c a$ from $- a c$ .

Tap for more steps...

Step 5.1

Move $c$ .

$a^{2} + 2 a b + b^{2} - b c - a c - 1 a c - c b + c^{2}$

Step 5.2

Subtract $a c$ from $- a c$ .

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

Step 6

Subtract $c b$ from $- b c$ .

Tap for more steps...

Step 6.1

Move $c$ .

$a^{2} + 2 a b + b^{2} - b c - 1 b c - 2 a c + c^{2}$

Step 6.2

Subtract $b c$ from $- b c$ .

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

Step 7

Move $- 2 b c$ .

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

Step 8

Move $b^{2}$ .

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