a) x4+5x3+10x-4=(x4-4)+(5x3+10x)=(x2-2)(x2+2)+5x(x2+2)
=(x2+2)(x2+5x-2)
b) =(x+y)3+z3-3xyz-3xy(x+y)
=(x+y+z)(x2+2xy+y2-yz-xz+z2)-3xy(z+x+y)
=(x+y+z)(x2+y2+z2+2xy-3xy-yz-xz)
=(x+y+z)(x2+y2+z2-xy-yz-xz)
phân tích đa thức thành nhân tử
a. x4+5x3+10x-4
\(=\left(x^4-4\right)+\left(5+x^3+10x\right)\)
\(=\left(x^2-2\right)\left(x^2+2\right)+5x\left(x^2+2\right)\)
\(=\left(x^2+2\right)\left(x^2+5x-2\right)\)
b. x3+y3+z3-3xyz
\(=\left(x+y+z\right)\left(x^2+2xy+y^2-yz-xz+z^2\right)-3xy\left(z+x+y\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2+2xy-3xy-yz-xz\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)
