Evaluate the product of $(x^{2} + y^{2}) (x^{2} - y^{2})$

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Solution

The given polynomials are $x^{2} + y^{2}$ and $x^{2} - y^{2}$ we multiply them as follows:

$(x^{2} + y^{2}) (x^{2} - y^{2}) = (x^{2} \times x^{2}) + (x^{2} \times - y^{2}) + (y^{2} \times x^{2}) + (y^{2} \times - y^{2}) = x^{4} - x^{2} y^{2} + x^{2} y^{2} - y^{4} = x^{4} - y^{4}$

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

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