Solve a(b+c-bc)-b(c+a-ac)-c(b+a) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Evaluate

$-2bc$

Solution Steps

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

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

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

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

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

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

Combine $ab$ and $-ba$ to get $0$.

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

The opposite of $-bac$ is $bac$.

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

Combine $-abc$ and $bac$ to get $0$.

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

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

$$ac-bc-\left(cb+ca\right)$$

To find the opposite of $cb+ca$, find the opposite of each term.

$$ac-bc-cb-ca$$

Combine $-bc$ and $-cb$ to get $-2bc$.

$$ac-2bc-ca$$

Combine $ac$ and $-ca$ to get $0$.

$$-2bc$$

Expand

$-2bc$

Solution Steps

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

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

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

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

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

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

Combine $ab$ and $-ba$ to get $0$.

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

The opposite of $-bac$ is $bac$.

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

Combine $-abc$ and $bac$ to get $0$.

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

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

$$ac-bc-\left(cb+ca\right)$$

To find the opposite of $cb+ca$, find the opposite of each term.

$$ac-bc-cb-ca$$

Combine $-bc$ and $-cb$ to get $-2bc$.

$$ac-2bc-ca$$

Combine $ac$ and $-ca$ to get $0$.

$$-2bc$$