\(\dfrac{1}{4}a^2+2ab^2+4b^4\)
= \(\left(\dfrac{1}{2}a\right)^2+2\cdot a\cdot\dfrac{1}{2}+\left(2b\right)^2\)
= \(\left(\dfrac{1}{2}a+2b\right)^2\)
= \(\left(\dfrac{1}{2}a+2b\right)\cdot\left(\dfrac{1}{2}a+2b\right)\)
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