А^4-а³+а-1=а³(а-1)+(а-1)=(а-1)(а³+1)=(а-1)(а+1)(а²-а+1)
х^6 - х^4 + 3x³+3x²=x^4(x²-1)+3x²(x+1)=x^4(x-1)(x+1)+3x²(x+1)=
=(x+1)(x^4(x-1)+3x²)=(x+1)(x^5-x^4+3x²)=(x+1)x²(x³-x²+3)=x²(x+1)(x³-x²+3)
(c+d)³-(c-d)³=(c+d-c+d)((c+d)²+(c+d)(c-d)+(c-d)²)=2d((c+d)²+c²-d²+(c-d)²)=
=2d(c²+2cd+d²+c²-d²+c²-2cd+d²)=2d(3c²+d²)
u²-v²-u+v=(u²-v²)-(u-v)=(u-v)(u+v)-(u-v)=(u-v)(u+v-1)
45m+6n-3mn-90=3m(15-n)+6(n-15)=3m(15-n)-6(15-n)=(15-n)(3m-6)=
=3(m-2)(15-n)
(y+z)^4 - (y-z)^4=y^4+4y³z+4yz³+6y²z²+z^4-y^4+4y³z+4yz³-6y²z²-z^4=
=8y³z+8yz³=8yz(y²+z²)