Question 85 (ii)

Expand the following, using suitable identities.

$(x^{2} y - x y^{2})^{2}$

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Solution

We have,
$(x^{2} y - x y^{2})^{2} = (x^{2} y)^{2} + (x y^{2})^{2} - 2 x^{2} y \times x y^{2}$
$= x^{4} y^{2} + x^{2} y^{4} - 2 x^{3} y^{3}$ [using the identity, $(a - b)^{2} = a^{2} + b^{2} - 2 a b$ ]

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