Question

Factor
`-(1)/(3)` out of
`4-(2)/(3)y`


`4-(2)/(3)y=-(1)/(3)` ( BLANK + BLANK
`y`)

Answer 1

`\bold{-(1)/(3)(-12 + 2y)}`

Explanation:

The original expression is

`4 - (2)/(3)y`

Let us write the factored result as

`-(1)/(3) (a + by)`

where a and b are constants to be determined

`-(1)/(3) (a + by) = -(1)/(3) (a) -(1)/(3) (by) = -(a)/(3) + -\frac{by} {3}`

Matching like terms to the original equation we get

`-(a)/(3) = 4`

Multiplying by -3 on both sides gives

a = -12

Matching the y terms we get

`-(by)/(3) = -(2)/(3)y` ==>
`-(b)/(3) = - (2)/(3)` ==> b = 2

So the factored expression is

`\bold{-(1)/(3)(-12 + 2y)}`

We can verify this if we multiply the terms inside the parentheses by
`-(1)/(3)`

`-(1)/(3)(-12) =4`

`-(1)/(3) (2y) = -(2)/(3)y`