Find: $(x^{2} - y^{2}) (x^{2} + y^{2})$

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Solution

We know that one of the identity is $(a - b) (a + b) = a^{2} - b^{2}$ .

Here, $a = x^{2}$ and $b = y^{2}$ . Now applying the identity we get:

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

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

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