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

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Solution

Using the identity is $(a + b) (a - b) = a^{2} - b^{2}$ .

Given: $(\frac{x}{3} + \frac{y}{2}) (\frac{x}{3} - \frac{y}{2})$ we apply the above identity by taking $a = x^{2}$ and $b = y^{2}$ :

We get, $(x^{2} + y^{2}) (x^{2} - y^{2}) = {(x^{2})}^{2} - {(y^{2})}^{2} = x^{4} - y^{4}$

Hence, $(x^{2} + y^{2}) (x^{2} - y^{2}) = x^{4} - y^{4}$ .

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