A perfect square trinomial is of the form
[tex](px+q)^2=p^2x^2+2pqx+q^2[/tex]
Consider
[tex]16m^2+48m+36[/tex]
This satisfies for p = 4 and q = 6. Hence it is a perfect square trinomial.
Consider
[tex]25a^2-45a+81[/tex]
This not satisfies as if we compare
[tex]\begin{gathered} a^2=25\Rightarrow a=5 \\ b^2=81\Rightarrow b=9 \end{gathered}[/tex]
but
[tex]2ab=2\cdot5\cdot9=90\ne45[/tex]
Hence it is not a perfect square trinomial.
Consider
[tex]9z^4+30z^2+25[/tex]
It can be written as
[tex]9(z^2)^2+30(z^2)+25[/tex]
Let
[tex]u=z^2[/tex]
Then the trinomial becomes
[tex]9u^2+30u+25[/tex]
This satisfies for p = 3 and q = 5. Hence it is a perfect square trinomial.
Consider
[tex]x^2-10x-16[/tex]
It is not in the perfect square trinomial form.
Hence it is not a perfect square trinomial.
