Question

Which facts could be applied to simplify this expression? Check all that apply. (-5x-3y)-(-x-3z).

To subtract like terms, subtract the coefficients, not the variables.
Like terms are terms that contain the same variable, raised to the same power.
The simplified expression is -6x-3y+3z.
Only combine terms which contain the same variable.
-(-x) is equivalent to -x, so -5x-x=-6x.
The simplified expression is -4x-3y+3z

Answer 1

The correct statements:

To subtract like terms, subtract the coefficients, not the variables

Like terms are terms that contain the same variable, raised to the same power

Only combine terms which contain the same variable (this one is confusing but it is true although the variable needs to be raised to the same power)

The simplified expression is -4x-3y+3z

Answer 2

The correct options are 1, 2, 4 and 6.

Explanation:

The given expression is

`(-5x-3y)-(-x-3z)`

To subtract like term subtract like terms, subtract the coefficients, not the variables.

Therefore option 1 is correct.

Like terms are terms that contain the same variable, raised to the same power. For example: 3xy and 5xy, 4x² and 3x².

Therefore, option 2 is correct.

Using distributive property we get

`-5x-3y-(-x)-(-3z)`

`-5x-3y+x+3z`

Only combine terms which contain the same variable.

Therefore option 4 is correct.

`(-5x+x)-3y+3z`

`-4x-3y+3z`

The simplified expression is -4x-3y+3z. Therefore option 6 is correct.