Factor ac(a+c)+ab(a-b)-bc(b+c)

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

Step 1

Apply the distributive property.

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

Step 2

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Step 3

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

Move $c$ .

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

Multiply $c$ by $c$ .

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

Step 4

Apply the distributive property.

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

Step 5

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Step 6

Rewrite using the commutative property of multiplication.

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

Step 7

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

Step 8

Apply the distributive property.

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

Step 9

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

Step 10

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

Move $c$ .

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

Multiply $c$ by $c$ .

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

Factor ac(a+c)+ab(a-b)-bc(b+c)

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