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Answer:
[tex]\bold{-\frac{1}{3}(-12 + 2y)}[/tex]
Step-by-step explanation:
The original expression is
[tex]4 - \frac{2}{3}y[/tex]
Let us write the factored result as
[tex]-\frac{1}{3} (a + by)[/tex]
where a and b are constants to be determined
[tex]-\frac{1}{3} (a + by) = -\frac{1}{3} (a) -\frac{1}{3} (by) = -\frac{a}{3} + -\frac{by} {3}[/tex]
Matching like terms to the original equation we get
[tex]-\frac{a}{3} = 4[/tex]
Multiplying by -3 on both sides gives
a = -12
Matching the y terms we get
[tex]-\frac{by}{3} = -\frac{2}{3}y[/tex] ==> [tex]-\frac{b}{3} = - \frac{2}{3}[/tex] ==> b = 2
So the factored expression is
[tex]\bold{-\frac{1}{3}(-12 + 2y)}[/tex]
We can verify this if we multiply the terms inside the parentheses by [tex]-\frac{1}{3}[/tex]
[tex]-\frac{1}{3}(-12) =4[/tex]
[tex]-\frac{1}{3} (2y) = -\frac{2}{3}y[/tex]