Question:
(1-x)^3
how does the above problem equal
-x^3 +3x^2 -3x +1
(1-x)^3 = (1-x)*(1-x)*(1-x)
We can then expand these brackets by multiplying the terms together.
The first two brackets multiplied together are below:
(1-x)*(1-x)
= (1*1) + (1*-x) + (1*-x) + (-x*-x)
= (1) + (-x) + (-x) + (x^2)
= 1 - 2x + x^2
re-inserting this back into the equation we see that:
(1-x)*(1 - 2x + x^2)
= (1*1) + (1*-2x) + (1*x^2) + (-x*1) + (-x*-2x) + (-x*x^2)
= (1) + (-2x) + (x^2) + (-x) + (2x^2) + (-x^3)
= 1 - 3x + 3x^3 - x^3
= -x^3 +3x^2 -3x +1
Hopefully this makes sense, if you need any clarification just ask.
Also any feedback on my way of explaining this would be greatly appreciated so I can better help people in the future.
+259 
