Question

Expand $(x-y{)}^3$

Answer 1

Expansion of algebric expression:

We know that $(x-y{)}^3$ can be written as

$(x-y)(x-y)(x-y)$

We know that $(x-y)(x-y)$ can be multiplied and written as

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

Hence,$(x-y{)}^3=x^3-y^3-3x^{2}y+3x{y}^2$