Question 1101495
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What kind of detail are you looking for?<br>
If {{{a^2-1+1/4a^2}}} is to be the square of a binomial (X+Y), then X squared has to be equal to a^2 (which means X is a), and Y^2 has to be 1/4a^2 (which means Y is 1/2a).<br>
Then, seeing that the middle term of the given expression is negative, we know the binomial we are looking for has to be {{{a - 1/2a}}}.<br>
This is verified when we square the binomial {{{a - 1/2a}}} and get {{{a^2-1+1/4a^2}}}.