For perfect square trinomial
[tex]\begin{gathered} c=(\frac{b}{2})^2,\text{ where b = coefficient of x is 8} \\ c=(\frac{8}{2})^2 \\ c=4^2 \\ c=16 \\ \text{Hence,} \\ x^2+8x+c=x^2+8x+16 \end{gathered}[/tex]As the square of a binomial, it is:
[tex]\begin{gathered} x^2+8x+16=(x^2+4x)+(4x+16) \\ \text{factorize,} \\ x(x+4)+4(x+4)=(x+4)(x+4) \\ \therefore x^2+8x+16=(x+4)^2 \end{gathered}[/tex]Therefore, the number added to make x²+8x a perfect square trinomial is 16.
As the square of a binomial, the perfect square trinomial is: (x+4)²
