Answer:
Fourth option is correct. We have to add 36 to change the given expression into a perfect square trinomial.
Step-by-step explanation:
The perfect square trinomial is
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The given expression is
[tex]x^2+12x[/tex] .... (1)
If an expression is defined as
[tex]ax^2+bx[/tex] ..... (2)
To change it into a perfect square trinomial we have to add [tex](\frac{-b}{2a})^2[/tex].
On comparing (1) and (2), we get
[tex]a=1[/tex]
[tex]b=12[/tex]
To change the given expression into a perfect square trinomial we have to add
[tex](\frac{-b}{2a})^2=(\frac{-12}{2(1)})^2=36[/tex]
[tex]x^2+12x+36=(x+6)^2[/tex]
Therefore to change the given expression into a perfect square trinomial we have to add 36 in the given expression.
