Simplify: ${(a^{2} - b^{2})}^{2}$

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Solution

Using identity for simplification of ${(a^{2} - b^{2})}^{2}$
Given: ${(a^{2} - b^{2})}^{2}$
Using the identity
$(a - b)^{2} = a^{2} + b^{2} - 2 a b$
${(a^{2} - b^{2})}^{2}$ $=$ ${(a^{2})}^{2}$ $+$ ${(b^{2})}^{2}$ $-$ $2 \times a^{2} \times b^{2}$
Therefore, ${(a^{2} - b^{2})}^{2}$ $=$ $a^{4} + b^{4} - 2 a^{2} b^{2}$ .

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