Question

What is the expanded form of ${\left(x-y\right)}^3$?

Answer 1

Determine the expanded form of ${\left(x-y\right)}^3$.

Since, ${\left(x-y\right)}^3$ is a cubic expression.

calculate ${\left(x-y\right)}^3$ by expanding as follow:

$\begin{array}{rcl}{\left(x-y\right)}^3& =& \left(x-y\right){\left(x-y\right)}^2\\ & \Rightarrow & {\left(x-y\right)}^3=\left(x-y\right)\left(x^2-2xy+y^2\right)\mathbf{}\left[\because {\left(x-y\right)}^2=x^2-2xy+y^2\right]\\ & \Rightarrow & {\left(x-y\right)}^3=x^3-2x^{2}y+x{y}^2-y{x}^2+2x{y}^2-y^3\\ & \Rightarrow & {\left(x-y\right)}^3=x^3-3x^{2}y+3x{y}^2-y^3\end{array}$

Hence, the required expanded form is$\begin{array}{l}{\left(x-y\right)}^3=x^3-3x^{2}y+3x{y}^2-y^3\end{array}$.