Please solve it step by step

(a^{2} + b^{2})^{2}

Notice that the binomial is being squared, so it expands to the following expression:

(a^{2} + b^{2})^{2} = (a^{2} + b^{2})(a^{2} + b^{2})

By the distributive property, while applying the product of exponents with like bases and combining like terms, we arrive at the following:

(a^{2} + b^{2})(a^{2} + b^{2}) = (a^{2} · a^{2}) + (a^{2} · b^{2}) + (b^{2} · a^{2}) + (b^{2} · b^{2})

= (a^{2+2}) + (a^{2}b^{2}) + (a^{2}b^{2}) + (b^{2+2})

= a^{4} + 2a^{2}b^{2} + b^{4}