Question

Simplifique as expressões.
a) (m - 1)² - (m + 1)(m - 1)
b) (x + 4)(x - 4) - (x - 4)²

Answer 1

$a) (m - 1)^2 - (m + 1)(m - 1)= \\ \\ (m-1)^2-(m^2-m+m-1) = \\ \\ (m-1)^2-(m^2-1) = \\ \\ (m^2-2m+1)-(m^2-1)=\\ \\ m^2-2m+1-m^2+1= \\ \\ \boxed{ -2m+2= -2(m-1) }$



$b) (x + 4)(x - 4) - (x - 4)^2= \\ \\ (x^2-4x+4x-4^2) -(x^2-8x+4^2)= \\ \\ x^2-16-(x^2-8x+16)= \\ \\ x^2-16-x^2+8x-16= \\ \\ 8x-32= \boxed{8(x-4)}$