a) \(x^4+2x^3+x^2=\left(x^2\right)^2+2.x^2.x+x^2=\left(x^2+x\right)^2\)
b) \(x^3-x+3x^2y+3xy^2+y^3-y=x^3+3x^2y+3xy^2+y^3-x-y\)
\(=\left(x-y\right)^3-\left(x+y\right)\)
c) \(5x^2-10xy+5y^2-20z^2=\left(\sqrt{5}x-\sqrt{5}y\right)^2-20z^2\)
Câu b :
\(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
Câu c :
\(5x^2-10xy+5y^2-20z^2\)
\(=5\left(x^2-2xy+y^2\right)-20z^2\)
\(=5\left(x-y\right)^2-20z^2\)
\(=5\left[\left(x-y\right)^2-4z^2\right]\)
\(=5\left(x-y+2z\right)\left(x-y-2z\right)\)
a) x4 + 2x3 + x2 =
= x2(x2 + 2x +1)
= x2(x + 1)2
b) x3 - x + 3x2 y + 3x y2 + y3 - y =
= ( x3 + 3x2 y + 3x y2 + y3 ) - ( x + y)
= ( x + y)3 - ( x + y)
= ( x + y) [ ( x + y )2 - 1]
= ( x + y) ( x + y - 1) ( x + y - 1)
c) 5x2 - 10 xy + 5y2 - 20z2 =
= 5( x2 - 2 xy + y2 - 4 z2 )
= 5[ ( x - y )2 - ( 2 z )2 ]
= 5( x - y - 2z )( x - y + 2z)
