Question
Find the following product:
$\left(x^2+x y+y^2\right)(x-y)$
$\left(x^2+x y+y^2\right)(x-y)$
✓
Answer
By column method:
$\text{x}^2+\text{xy}+\text{y}^2\\\underline{\ \ \ \ \times (\text{x}-\text{y})\ \ \ }\\\text{x}^3+\text{x}^2\text{y}+\text{xy}^2\\ \underline{\ \ \ \ -\text{x}^2\text{y}-\text{xy}^2-\text{y}^3}\\ \text{x}^3-\text{y}^3$
$\therefore(\text{x}^2+\text{xy}+\text{y}^2)(\text{x}-\text{y})=\text{x}^3-\text{y}^3$
$\text{x}^2+\text{xy}+\text{y}^2\\\underline{\ \ \ \ \times (\text{x}-\text{y})\ \ \ }\\\text{x}^3+\text{x}^2\text{y}+\text{xy}^2\\ \underline{\ \ \ \ -\text{x}^2\text{y}-\text{xy}^2-\text{y}^3}\\ \text{x}^3-\text{y}^3$
$\therefore(\text{x}^2+\text{xy}+\text{y}^2)(\text{x}-\text{y})=\text{x}^3-\text{y}^3$
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