Question

Phân tích đa thức thành nhân tử :

a ) \(x^3z+x^2yz-x^2z^2-xyz^2\) b ) \(p^{m+2}q-p^{m+1}q^3-p^2q^{n+1}+pq^{n+3}\)

Answer 1

a ) \(x^3z+x^2yz-x^2z^2-xyz^2=\left(x^3z-x^2z^2\right)+\left(x^2yz-xyz^2\right)\)

\(=\left(x-z\right)\left(x^2z+xyz\right)\)

\(=xz\left(x-z\right)\left(x+y\right)\)

b ) \(p^{m+2}.q-p^{m+1}q^3-p^2q^{n+1}+pq^{n+3}\)

\(=p^{m+1}q\left(p-q^2\right)-pq^{n+1}\left(p-q^2\right)\)

\(=\left(p-q^2\right)\left(p^{m+1}q-pq^{n+1}\right)\)

\(=pq\left(p-q^2\right)\left(p^m-q^n\right)\)