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in Algebraic Expressions by (26.3k points)
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Factorize:

x(x3–y3)+3xy-(x–y)

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Best answer

Given,

\(\text{x}(\text{x}^3-\text{y}^{3})+3\text{x}\text{y}-(\text{x}-\text{y})\)

As \((\text{x}^{3}-\text{y}^{3})=(\text{x}-\text{y})(\text{x}^{2}+\text{x}\text{y}\,+\text{y}^{2})\)

\(\text{x}(\text{x}^{3}-\text{y}^{3})+3\text{xy}-(\text{x-y})\) = \(\text{x}[(\text{x-y})(\text{x}^{2}+\text{xy}\,+\text{y}^{2})\,+3\text{xy}-(\text{x-y})\)

Take \(\text{x}(\text{x-y})\) common to get,

\(\text{x}(\text{x-y})[(\text{x}^{2}+\text{x}+\text{y}^{2})+3\text{y}]\)

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