Respuesta :
Answer:
Perfect square trinomial: [tex]n^2+n+\dfrac{1}{4}[/tex]
Binomial squared: [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].
Step-by-step explanation:
The given expression is [tex]n^2+n.[/tex]
Here coefficient of n is 1.
Now, find square of half of coefficient of n.
[tex]\left(\dfrac{1}{2}\times 1\right)^2=\dfrac{1}{4}[/tex]
Now, add [tex]\dfrac{1}{4}[/tex] in the expression to make it perfect square trinomial.
[tex]n^2+n+\dfrac{1}{4}[/tex]
[tex]\Rightarrow n^2+n+\left(\dfrac{1}{2}\right)^2[/tex]
[tex]\Rightarrow \left(n+\dfrac{1}{2}\right)^2[/tex] [tex]\because (a+b)^2=a^2+2ab+b^2[/tex]
Therefore, perfect square trinomial is [tex]n^2+n+\dfrac{1}{4}[/tex] and binomial squared is [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].
