Question

(1+x) (x-1)-(4+x)(x-4)

Answer 1

(x+1) (x-1)-(x+4)(x-4)
$x^{2}$  - 1 -(  $x^{2}$- 16)
 $x^{2}$ - 1 - $x^{2}$ + 16
-1 +16
15 

Answer 2

(1+x) (x-1)-(4+x)(x-4)= (x-1)(x-1) - (x+4) (x-4)
Conociendo el producto notable: (a+b)(a-b)= a²-b²

(x-1)(x-1) - (x+4) (x-4) = x² - 1² - ( x²-4²)
= x²-1 - (x² -16) = x² -1 -x² + 16 = 15

(1+x) (x-1)-(4+x)(x-4) = 15