Question

Expand binomial using binomial expansion (x-y)^3

Answer 1

The expression is,

$(x-y)^3$

Expanding the expression we get,

$(x-y)^3=(x-y)(x-y)^2\ldots.(1)$

We have,

$(x-y)^2=x^2-2xy+y^2\ldots..(2)$

Substituting equation 2 in equation 1, we get,

$\begin{gathered} (x-y)^3=(x-y)(x^2-2xy+y^2) \\ \text{ =}x(x^2-2xy+y^2)-y(x^2-2xy+y^2) \\ \text{ =}x^3-2x^2y+xy^2-yx^2+2xy^2-y^3 \\ \text{ =x}^3-y^3+3xy^2-3x^2y \end{gathered}$