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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Multiply $a^{2}$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a^{2}$ .

Raise $a$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

$- a^{3} b^{2} c^{2} - a^{2} b^{2} c^{2} b - a^{2} b^{2} c^{2} (- c)$

Multiply $b^{2}$ by $b$ by adding the exponents.

Move $b$ .

$- a^{3} b^{2} c^{2} - a^{2} (b \cdot b^{2}) c^{2} - a^{2} b^{2} c^{2} (- c)$

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

Raise $b$ to the power of $1$ .

$- a^{3} b^{2} c^{2} - a^{2} (b^{1} b^{2}) c^{2} - a^{2} b^{2} c^{2} (- c)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- a^{3} b^{2} c^{2} - a^{2} b^{1 + 2} c^{2} - a^{2} b^{2} c^{2} (- c)$

Add $1$ and $2$ .

$- a^{3} b^{2} c^{2} - a^{2} b^{3} c^{2} - a^{2} b^{2} c^{2} (- c)$

Multiply $c^{2}$ by $c$ by adding the exponents.

Move $c$ .

$- a^{3} b^{2} c^{2} - a^{2} b^{3} c^{2} - a^{2} b^{2} (c \cdot c^{2}) \cdot - 1$

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

Raise $c$ to the power of $1$ .

$- a^{3} b^{2} c^{2} - a^{2} b^{3} c^{2} - a^{2} b^{2} (c^{1} c^{2}) \cdot - 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- a^{3} b^{2} c^{2} - a^{2} b^{3} c^{2} - a^{2} b^{2} c^{1 + 2} \cdot - 1$

Add $1$ and $2$ .

$- a^{3} b^{2} c^{2} - a^{2} b^{3} c^{2} - a^{2} b^{2} c^{3} \cdot - 1$

Step 3

Multiply $- a^{2} b^{2} c^{3} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$- a^{3} b^{2} c^{2} - a^{2} b^{3} c^{2} + 1 a^{2} b^{2} c^{3}$

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

$- a^{3} b^{2} c^{2} - a^{2} b^{3} c^{2} + a^{2} b^{2} c^{3}$