Answer:
x^3 - 6x^2y - 12xy^2 - 8y^3
Step-by-step explanation:
(x-2y)^3
There are three parts to binomial expansion - the coefficient, the power of the first term and the power of the second term.
Use Pascal's Triangle to find the coefficient.
^3 = 1 3 3 1
The first term's powers are descending:
x^3 x^2 x^1 x^0
The second term's powers are ascending.
-2y^0 -2y^1 -2y^2 -2y^3
The first coefficient is multiplied by the first power of the first term and the first power of the second term.
3C0 x^3 (-2y)^0 = 1 x^3 1 = x^3
2C1 x^2 (-2y)^1 = 3 x^2 -2y = -6x^2y
1C2 x^1 (-2y)^2 = 3 x -2y^2 = -12xy^2
0C3 x^0 (-2y)^3 = 1 1 -2y^3 = -8y^3
