ANSWER
[tex] {x}^{2} - 2x + 1[/tex]
and
[tex] {x}^{2} + 2x + 1[/tex]
EXPLANATION
A perfect square trinomial can be written in the form:
[tex](a - b) ^{2} = {a}^{2} - 2(ab) + {b}^{2} [/tex]
or
[tex](a + b) ^{2} = {a}^{2} + 2(ab) + {b}^{2} [/tex]
For the first option;
[tex](x + 1) ^{2} = {x}^{2} + 2(x)(1)) + {1}^{2} [/tex]
This is a perfect square trinomial.
For the second option,
[tex](x - 1)^{2} = {x}^{2} - 2(x)(1)) + {1}^{2} [/tex]
This is also a perfect square trinomial.
The third option
[tex]4 {x}^{2} + 12x + 16[/tex]
This cannot be written as a perfect square.
[tex]4 {x}^{2} - 12x - 9[/tex]
This cannot also be written as a perfect square.
