Question

Resolva as operação e indicadas e apresente a resposta na forma reduzida:
  a)        (2x -1)² + (x +3) (x -3)
  b)        (a³ -1)²  - (a3 -a) .(a³ +a) + (a³ -1)²
 

Answer 1

$a)\;(2x -1)^2+(x +3)(x -3)=4x^2-4x+1+x^2-9=5x^2-4x-8\\\\\Longrightarrow(2x -1)^2+(x +3)(x -3)=5x^2-4x-8\\\\\\\\ b)\;(a^3 -1)^2-(a^3 -a)(a^3 +a)+(a^3-1)^2\\\\=a^6-2a^3+1-(a^6-a^2)+a^6-2a^3+1\\\\ =a^6-2a^3+1-a^6+a^2+a^6-2a^3+1=a^6-4a^3+a^2+2\\\\\Longrightarrow(a^3 -1)^2-(a^3 -a)(a^3 +a)+(a^3-1)^2=a^6-4a^3+a^2+2$