Question

Grupand convenabil, descompuneti in factori: a) ac-ad+bc-bd , b) x³+x²z+2xz²+2z³ , c) x³-x²z+2xz²-2z³ , d) x³+x²z-2xz²-2z³ , e) a³+2a²+2a+4 si f) a³-2a²+2a-4

Answer 1

a) ac-ad+bc-bd =a(c-d)+b(c-d)=(c-d)(a+b)
b) x³+x²z+2xz²+2z³ =x²(x+z)+2z²(x+z)=(x+z)(x²+2z²)
c) x³-x²z+2xz²-2z³ =x²(x-z)+2z²(x-z)=(x-z)(x²+2z²)
d) x³+x²z-2xz²-2z³  =x²(x+z)-2z²(x+z)=(x+z)(x²-2z²)=(x+z)(x+z√2)(x-z√2)
e) a³+2a²+2a+4  =a²(a+2)+2(a+2)=(a+2)(a²+2)
f) a³-2a²+2a-4 =a²(a-2)+2(a-2)=(a-2)(a²+2)