a) \(x^3-2x^2+x\)
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
b) \(a^4+a^3+a^3b+a^2b\)
\(=a^2\left(a^2+a+ab+b\right)\)
\(=a^2\left[a\left(a+b\right)+\left(a+b\right)\right]\)
\(=a^2\left(a+1\right)\left(a+b\right)\)
\(a^3+3a^2+4a+12\)
\(=a^2\left(a+3\right)+4\left(a+3\right)\)
\(=\left(a^2+4\right)\left(a+3\right)\)
d) \(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x-2y+3\right)\left(-4y-x+5\right)\)
e) \(27x^3+27x^2+9x+1\)
\(=\left(3x+1\right)^3\)
Áp dụng HĐT: \(\left(A+B\right)^3=A^3+3A^2B+3AB^2+B^3\)
f) \(x^3z+x^2yz-x^2z^2-xyz^2\)
\(=x^2z\left(x+y\right)-xz^2\left(x+y\right)\)
\(=\left(x^2z-xz^2\right)\left(x+y\right)\)
\(=xz\left(x-z\right)\left(x+y\right)\)
