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Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n2+n

User Rahulrvp
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Answer:

Perfect square trinomial:
n^2+n+(1)/(4)

Binomial squared:
\left(n+(1)/(2)\right)^2.

Explanation:

The given expression is
n^2+n.

Here coefficient of n is 1.

Now, find square of half of coefficient of n.


\left((1)/(2)* 1\right)^2=(1)/(4)

Now, add
(1)/(4) in the expression to make it perfect square trinomial.


n^2+n+(1)/(4)


\Rightarrow n^2+n+\left((1)/(2)\right)^2


\Rightarrow \left(n+(1)/(2)\right)^2
\because (a+b)^2=a^2+2ab+b^2

Therefore, perfect square trinomial is
n^2+n+(1)/(4) and binomial squared is
\left(n+(1)/(2)\right)^2.

User Nick Mazurkin
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