Question

Descompuneti in factori:
a)a-b+b²-a²;
b)x²-x-y²-y;
c)x+y-x³-y³;
d)a³-b³+b-a.

Answer 1

a)  a-b-a²+b² = a-b - (a²-b²) = a-b -(a+b)(a-b) = (a-b)(1-a-b) ;
b)  x²-y² - (x+y) = (x+y)(x-y) - (x+y) = (x+y)(x-y-1) ;
c)  x+y - (x³+y³) = x+y - (x+y)(x²-xy+y²) = (x+y)(1 - x²+xy-y²) ;
d) a³-b³ -a+b = (a-b)(a²+ab+b²) - (a-b) = (a-b)(a²+ab+b²-1) ;