Question

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

Answer 1

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`.