Question

Dados os polinômios
A= y²-2y +1, B= y+1 e C= -y+1 , calcule
1) AB-C
2) A-BC
3) (A+B) (B+C)

Answer 1

A= y²-2y +1, B= y+1 e C= -y+1 

1)
$AB-C=\\(y^2-2y+1)(y+1)-(-y+1)=\\(y-1)^2(y+1)+y-1=\\(y-1)(y-1)(y+1)+y-1=\\(y-1)(y^2-1)+y-1=\\y^3-y-y^2+1+y-1=\\y^3-y^2$

2)
$A-BC=\\y^2-2y+1-(y+1)(-y+1)=\\y^2-2y+1-(y+1)(-y+1)=\\y^2-2y+1-(-y^2+1)=\\y^2-2y+1+y^2-1=\\2y^2-2y$

3)
$(A+B) (B+C)=\\(y^2-2y+1+y+1)(y+1+(-y+1))=\\(y^2-y+2)(y+1-y+1)=\\(y^2-y+2)2=\\2y^2-2y+4$