a)
\(5x^3-12x^2+14x-4=5x^3-2x^2-10x^2+4x+10x-4\)
\(=x^2(5x-2)-2x(5x-2)+2(5x-2)\)
\(=(5x-2)(x^2-2x+2)\)
b)
\((x+y+z)^3-x^3-y^3-z^3\)
\(=(x+y)^3+z^3+3(x+y)^2z+3(x+y)z^2-x^3-y^3-z^3\)
\(=x^3+y^3+3xy(x+y)+z^3+3(x+y)z(x+y+z)-x^3-y^3-z^3\)
\(=3(x+y)[xy+z(x+y+z)]=3(x+y)[(xy+zx)+z(y+z)]\)
\(=3(x+y)[x(y+z)+z(y+z)]=3(x+y)(y+z)(x+z)\)
c)
Đặt $(a+b-c,b+c-a,c+a-b)=(x,y,z)$
Ta có:
\((a-b+c)^3-(a-b-c)^3-(c-a-b)^3-(a+b+c)^3\)
\(=(a+c-b)^3+(b+c-a)^3+(a+b-c)^3-(a+b+c)^3\)
\(=z^3+y^3+x^3-(x+y+z)^3\)
\(=-3(x+y)(y+z)(z+x)\) (kết quả phần b)
\(=-3(2b)(2c)(2a)=-24abc\)
