SOLUTION: Q. Express the following as the square of a binomial. 1. a^2-1+1/4a^2 Please show me in detail. Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Q. Express the following as the square of a binomial. 1. a^2-1+1/4a^2 Please show me in detail. Thank you.       Log On


   

Question 1101495: Q. Express the following as the square of a binomial.
1. a^2-1+1/4a^2
Please show me in detail. Thank you.
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


What kind of detail are you looking for?

If a%5E2-1%2B1%2F4a%5E2 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).

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%2F2a.

This is verified when we square the binomial a+-+1%2F2a and get a%5E2-1%2B1%2F4a%5E2.