Simplify (a-b-c)^2

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

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

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

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

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

Simplify each term.

Multiply $a$ by $a$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $b$ by $1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $c$ by $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $c$ .

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

Multiply $c$ by $c$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

Move $b$ .

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

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

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

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

Move $c$ .

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

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

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

Add $b c$ and $c b$ .

Reorder $c$ and $b$ .

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

Add $b c$ and $b c$ .

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

Move $2 b c$ .

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

Move $b^{2}$ .

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

Simplify (a-b-c)^2

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