Question

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Answer 1

$\frac{1}{4}a^{4}+2a^{2}b^{2}+4b^{4}=(\frac{1}{2}a^{2})^{2}+2*\frac{1}{2}a^{2}*2b^{2}+(2b^{2})^{2}=(\frac{1}{2}a^{2}+2b^{2})^{2}=(\frac{1}{2}a^{2}+2b^{2})(\frac{1}{2}a^{2}+2b^{2})$