Solve a-[-(b-c)+2(a-c)+2(b-2))

$$a - [ - ( b - c ) + 2 ( a - c ) + 2 ( b - 2 ) )$$

Evaluate

$$4+c-b-a$$

Solution Steps

To find the opposite of b-c, find the opposite of each term.

$$a-\left(-b-\left(-c\right)+2\left(a-c\right)+2\left(b-2\right)\right)$$

The opposite of -c is c.

$$a-\left(-b+c+2\left(a-c\right)+2\left(b-2\right)\right)$$

Use the distributive property to multiply 2 by a-c.

$$a-\left(-b+c+2a-2c+2\left(b-2\right)\right)$$

Combine c and -2c to get -c.

$$a-\left(-b-c+2a+2\left(b-2\right)\right)$$

Use the distributive property to multiply 2 by b-2.

$$a-\left(-b-c+2a+2b-4\right)$$

Combine -b and 2b to get b.

$$a-\left(b-c+2a-4\right)$$

To find the opposite of b-c+2a-4, find the opposite of each term.

$$a-b-\left(-c\right)-2a-\left(-4\right)$$

The opposite of -c is c.

$$a-b+c-2a-\left(-4\right)$$

The opposite of -4 is 4.

$$a-b+c-2a+4$$

Combine a and -2a to get -a.

$$-a-b+c+4$$

Expand

$$4+c-b-a$$

Solution Steps

To find the opposite of b-c, find the opposite of each term.

$$a-\left(-b-\left(-c\right)+2\left(a-c\right)+2\left(b-2\right)\right)$$

The opposite of -c is c.

$$a-\left(-b+c+2\left(a-c\right)+2\left(b-2\right)\right)$$

Use the distributive property to multiply 2 by a-c.

$$a-\left(-b+c+2a-2c+2\left(b-2\right)\right)$$

Combine c and -2c to get -c.

$$a-\left(-b-c+2a+2\left(b-2\right)\right)$$

Use the distributive property to multiply 2 by b-2.

$$a-\left(-b-c+2a+2b-4\right)$$

Combine -b and 2b to get b.

$$a-\left(b-c+2a-4\right)$$

To find the opposite of b-c+2a-4, find the opposite of each term.

$$a-b-\left(-c\right)-2a-\left(-4\right)$$

The opposite of -c is c.

$$a-b+c-2a-\left(-4\right)$$

The opposite of -4 is 4.

$$a-b+c-2a+4$$

Combine a and -2a to get -a.

$$-a-b+c+4$$