Answer:
[tex] - (x - 4 {)}^{2} [/tex]
Step-by-step explanation:
The given expresion is
[tex] - {x}^{2} + 8x - 16[/tex]
Factor -1;
[tex] - ( {x}^{2} - 8x + 16)[/tex]
Split the middle term with -4x-4x
[tex] - ( {x}^{2} - 4x - 4x + 16)[/tex]
Factor by grouping within the parenthesis:
[tex] - ( x({x} - 4)- 4(x - 4) )[/tex]
Factor further:
[tex] - (x - 4)(x -4 )[/tex]
[tex] - (x - 4 {)}^{2} [/tex]
This the opposite of the square of (x-4)
