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
\((a+b)^2=a^2+2ab+b^2\)
The given expression is
\(x^2+12x\) .... (1)
If an expression is defined as
\(ax^2+bx\) ..... (2)
To change it into a perfect square trinomial we have to add \((\frac{-b}{2a})^2\).
On comparing (1) and (2), we get
\(a=1\)
\(b=12\)
To change the given expression into a perfect square trinomial we have to add
\((\frac{-b}{2a})^2=(\frac{-12}{2(1)})^2=36\)
\(x^2+12x+36=(x+6)^2\)
Therefore to change the given expression into a perfect square trinomial we have to add 36 in the given expression.
