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Factorisation by Regrouping Terms

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Question

Solve : $(x^{2} - y^{2}) \times (x + 2 y)$

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Solution

Let us multiply the given binomials $(x^{2} - y^{2})$ and $(x + 2 y)$ as shown below:

$(x^{2} - y^{2}) (x + 2 y) = x^{2} (x + 2 y) - y^{2} (x + 2 y) = (x^{2} \times x) + (x^{2} \times 2 y) - (y^{2} \times x) - (y^{2} \times 2 y) = x^{3} + 2 x^{2} y - x y^{2} - 2 y^{3}$

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

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