Question

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

Answer 1

Answer:

Perfect square trinomial: $n^2+n+\dfrac{1}{4}$

Binomial squared: $\left(n+\dfrac{1}{2}\right)^2$.

Step-by-step explanation:

The given expression is $n^2+n.$

Here coefficient of n is 1.

Now, find square of half of coefficient of n.

$\left(\dfrac{1}{2}\times 1\right)^2=\dfrac{1}{4}$

Now, add $\dfrac{1}{4}$ in the expression to make it perfect square trinomial.

$n^2+n+\dfrac{1}{4}$

$\Rightarrow n^2+n+\left(\dfrac{1}{2}\right)^2$

$\Rightarrow \left(n+\dfrac{1}{2}\right)^2$      $\because (a+b)^2=a^2+2ab+b^2$

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