Answer:
C. [tex]x^2 - 4x + 4[/tex]
D. [tex]x^2 +10x +25[/tex]
Step-by-step explanation:
A trinomial [tex]ax^2+bx+c[/tex] is perfect square trinomial if,
[tex]D=b^2 - 4ac = 0[/tex],
A. [tex]x^2 -9[/tex]
By comparing,
a = 1, b = 0, c = -9,
[tex]0^2 - 4\times 1\times -9\neq 0[/tex]
⇒ it is not a perfect square trinomial.
B. [tex]x^2 -100[/tex]
By comparing,
a = 1, b = 0, c = -100,
[tex]0^2 - 4\times 1\times -100\neq 0[/tex]
⇒ it is not a perfect square trinomial.
C. [tex]x^2 - 4x + 4[/tex]
By comparing,
a = 1, b = -4, c = 4,
[tex](-4)^2 - 4\times 1\times 4=16-16=0[/tex]
⇒ it is a perfect square trinomial.
D. [tex]x^2 +10x +25[/tex]
By comparing,
a = 1, b = 10, c = 25,
[tex]10^2 - 4\times 1\times 25=100-100=0[/tex]
⇒ it is a perfect square trinomial.
E. [tex]x^2 +15x + 36[/tex]
By comparing,
a = 1, b = 15, c = 36,
[tex]15^2 - 4\times 1\times 36=225-144=81\neq 0[/tex]
⇒ it is not a perfect square trinomial.
