Solve a(b+c)-b(a+c)+c(b-a)

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

Evaluate

$$0$$

Solution Steps

Use the distributive property to multiply a by b+c.

$$ab+ac-b\left(a+c\right)+c\left(b-a\right)$$

Use the distributive property to multiply b by a+c.

$$ab+ac-\left(ba+bc\right)+c\left(b-a\right)$$

To find the opposite of ba+bc, find the opposite of each term.

$$ab+ac-ba-bc+c\left(b-a\right)$$

Combine ab and -ba to get 0.

$$ac-bc+c\left(b-a\right)$$

Use the distributive property to multiply c by b-a.

$$ac-bc+cb-ca$$

Combine -bc and cb to get 0.

$$ac-ca$$

Combine ac and -ca to get 0.

$$0$$

Factor

$$0$$