Question

All of the following expressions are equivalent to 12w + 6, except:

-1(12w - 6)
(3 + 6w)2
6(1 + 2w)
-1(-12w - 6)

Answer 1

-1(-12w - 6)

Explanation:

Answer 2

`-1(12w-6)`

Explanation:

we have

`(12w+6)`

Verify each expression

case 1)
`-1(12w-6)`

Apply distributive property

Remember that

`(-1)(-1)=1`

`(-1)(1)=-1`

`-1(12w)-1(-6)`

`-12w+6`

compare with the given expression

`-12w+6 \\eq (12w+6)` ----> are not equivalent

case 2)
`2(3+6w)`

Apply distributive property

`2(3)+2(6w)`

`6+12w`

compare with the given expression

`6+12w=(12w+6)` ---> are equivalent

case 3)
`6(1+2w)`

Apply distributive property

`6(1)+6(2w)`

`6+12w`

compare with the given expression

`6+12w=(12w+6)` ---> are equivalent

case 4)
`-1(-12w-6)`

Apply distributive property

Remember that

`(-1)(-1)=1`

`(-1)(1)=-1`

`-1(-12w)-(1)(-6)`

`12w+6`

compare with the given expression

`12w+6=(12w+6)` ---> are equivalent