Explicație pas cu pas:
(x-3)(x-1)(x+1)(x+3)+15=(x²-1)(x²-9)+15=x⁴-x²-9x²+9+15=
x⁴-10x²+24=x⁴-6x²-4x²+24=x²(x²-6)-4(x²-6)=(x²-6)(x²-4)=
(x+2)(x-2)(x²-6)
x(x²+3x+4)(x+3)+4=(x²+3x)(x²+3x+4)+4
Notam t=x²+3x
t(t+4)+4=t²+4t+4=(t+2)²=(x²+3x+2)²=(x²+x+2x+2)²=
[x(x+1)+2(x+1)]²=[(x+1)(x+2)]²=(x+1)²*(x+2)²
(x²+x-1)+3(x²+x-1)+2=(x²+x-1)(1+3)+2=4(x²+x-1)+2=
4x²+4x-4+2=4x²+4x+2
