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x2 + 2xy - 8y2 + 2xz + 14yz - 3z2
= ( x2 + y2 +z2 + 2xy + 2yz ) + ( -9x2 + 12yz - 4x2 )
= ( x + y +z )2 - [ (3x)2 - 2.3.x.2y + ( 2x)2
= ( x + y +z )2 - ( 3y - 2x)2
= ( x + y +z - 3y + 2x )(x+ y + z + 3y - 2x )
a) x^3 +5x^2+6x
= x^3+2x^2+3x^2+6x
=x*(x+3)*(x+2)
b) x^2-6x+8
= x^2-2x-4x+8
=(x-2)*(x-4)
c)2x^2+98+28x-8y^2
=2(x^2+14x+49-4y^2)
=2*[(x+7)^2-4y^2]
2*(x-7-2y)*(x-7+2y)
a) x2 + 2x2 + 3x2 + 6x
= x( x+2 ) + 3( x+2 )
=(x+3)(x+2)
b) x2 - 2x - 4x + 8
=x(x-2)-4(x-2)
=(x-4)(x-2)
c)
x\(^2\)-(a+b)x+ab
= x\(^2\)-ax-bx+ab
= x(x-a) - b(x-a)
= ( x-a).( x-b)
ax-2x-a\(^2\)+2a
= x(a-2) - a(a-2)
= (a-2).( x-a)
Sửa đề: \(x^4+x^2+1\)
\(=x^4+2x^2+1-x^2\)
\(=\left(x^2+1\right)^2-x^2\)
\(=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
\(x^2+2xy-8y^2+2xz+14yz-3z^2\)
\(=\left(x^2+y^2+z^2+2xy+2xz+2yz\right)+\left(-9x^2+12yz-4x^2\right)\)
\(=\left(x+y+z\right)^2-\left[\left(3x\right)^2-2.3x.2y+\left(2x\right)^2\right]\).
\(=\left(x+y+z\right)^2-\left(3y-2x\right)^2\)
\(=\left(x+y+z-3y+2x\right)\left(x+y+z+3y-2x\right)\)