Question

Phân tích đa thức sau thành nhân tử:
a) x² +4x -y² +4
b) 3x² +6xy +3y² -3z2
c) x² -2xy +y² -z² +2zt -t²

Answer 1

a) \(x^2+4x-y^2+4=\left(x^2+4x+4\right)-y^2\)

\(\left(x+2\right)^2-y^2=\left(x+2-y\right).\left(x+2+y\right)\)

b) \(3x^2+6xy+3y^2-3z^2\Leftrightarrow\left(\sqrt{3}x+\sqrt{3}y\right)^2-\left(\sqrt{3}z\right)^2\)

\(\Leftrightarrow\left(\sqrt{3}x+\sqrt{3}y-\sqrt{3}z\right).\left(\sqrt{3}x+\sqrt{3}y+\sqrt{3}z\right)\)

c) \(x^2-2xy+y^2-z^2+2zt-t^2\Leftrightarrow\left(x^2-2xy+y^2\right)-\left(z^2-2zt+t^2\right)\)

\(\Leftrightarrow\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\)