Bài 6:
a: \(x^5+x+1\)
\(=x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
b: \(x^3+y^3+z^3-3xyz\)
\(=\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left[x^2+2xy+y^2-xz-zy+z^2-3xy\right]\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-xz-yz\right)\)
Bài 7:
a: \(3x^3-75x\)
\(=3x\cdot x^2-3x\cdot25\)
\(=3x\left(x^2-25\right)=3x\left(x-5\right)\left(x+5\right)\)
b: \(5x^2y-30xy^2+45y^3\)
\(=5y\cdot x^2-5y\cdot6xy+6y\cdot9y^2\)
\(=5y\left(x^2-6xy+9y^2\right)=5y\left(x-3y\right)^2\)
