The binomial expansion of (x-2y) ^3 is?

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

x^3 - 6x^2y + 12xy^2 - 8y^3

Step-by-step explanation:

(x-2y) ^3

= (x - 2y) (x - 2y) ^2

= (x - 2y) (x^2 - 4xy + 4y^2)

= x^3 - 4x^2y + 4xy^2 - 2x^2y + 8xy^2 - 8y^3

= x^3 - 6x^2y + 12xy^2 - 8y^3