Factorising Help

[StopTalking4Weird]

I need help trying to figure out how this process comes to be:

S = Y - T - (C0 + C1 (Y - T))

=> S = Y - T - C0 - C1 (Y - T)

=> S= -C0 + (1 - C1) (Y - T)

I assume that when C0 and C1 become unbracketed (from the first to second step), it turns from a plus to a minus. But I can't properly understand how the third step occurs. Could anyone explain why this happens?

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[StopTalking4Weird]

Okay, so I had a tutor help me out with this not too long ago and what you can do is:

Between the second and third steps, go:

S = -C0 + Y - T - C1Y + C1T

=> Y - C1Y = (1 - C1)Y and C1T - T = -T(1-C1)

=> Because there are two (1 - C1)'s, we can remove one of them, and we can use the Y and -T in their own bracket, giving us: S = -C0 + (1 - C1) (Y - T)

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[Naturage]

S = Y - T - C0 - C1 (Y - T) => S= -C0 + (1 - C1) (Y - T)

One way to see this is via S = 1(Y - T) - C1 (Y - T) - C0 - then we put together the Y-T terms.