Question

Rewrite as the opposite of the square of a binomial: −x^2+8x−16

Answer 1

Answer:

$- (x - 4 {)}^{2}$

Step-by-step explanation:

The given expresion is

$- {x}^{2} + 8x - 16$

Factor -1;

$- ( {x}^{2} - 8x + 16)$

Split the middle term with -4x-4x

$- ( {x}^{2} - 4x - 4x + 16)$

Factor by grouping within the parenthesis:

$- ( x({x} - 4)- 4(x - 4) )$

Factor further:

$- (x - 4)(x -4 )$

$- (x - 4 {)}^{2}$

This the opposite of the square of (x-4)