e: Ta có: \(x^5-5x^3+4x\)

\(=x\left(x^4-5x^2+4\right)\)

\(=x\left(x^2-1\right)\left(x^2-4\right)\)

\(=x\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)

bn gõ bài trong công thức trực quan ik, khó nhìn lắm, ko làm đc

1) \(x^2y^2\left(y-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)

\(=x^2y^3-x^3y^2+y^2z^3-y^3z^2-z^2x^2\left(z-x\right)\)

\(=\left(y^2z^3-x^3y^2\right)-\left(y^3z^2-x^2y^3\right)-z^2x^2\left(z-x\right)\)

\(=y^2\left(z^3-x^3\right)-y^3\left(z^2-x^2\right)-z^2x^2\left(z-x\right)\)

\(=y^2\left(z-x\right)\left(z^2+zx+x^2\right)-y^3\left(z-x\right)\left(z+x\right)-z^2x^2\left(z-x\right)\)

\(=\left(z-x\right)\left[y^2\left(z^2+zx+x^2\right)-y^3\left(z+x\right)-z^2x^2\right]\)

\(=\left(z-x\right)\left[\left(y^2z^2+xy^2z+x^2y^2\right)-\left(y^3z+xy^3\right)-z^2x^2\right]\)

\(=\left(z-x\right)\left(y^2z^2+xy^2z+x^2y^2-y^3z-xy^3-z^2x^2\right)\)

\(=\left(z-x\right)\left[\left(y^2z^2-y^3z\right)-\left(x^2z^2-x^2y^2\right)+\left(xy^2z-xy^3\right)\right]\)

\(=\left(z-x\right)\left[y^2z\left(z-y\right)-x^2\left(z^2-y^2\right)+xy^2\left(z-y\right)\right]\)

\(=\left(z-x\right)\left[y^2z\left(z-y\right)-x^2\left(z-y\right)\left(z+y\right)+xy^2\left(z-y\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left[y^2z-x^2\left(z+y\right)+xy^2\right]\)

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

\(=\left(z-x\right)\left(z-y\right)\left[\left(y^2z-x^2z\right)-\left(x^2y-xy^2\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left[z\left(y^2-x^2\right)-xy\left(x-y\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left[z\left(y-x\right)\left(y+x\right)+xy\left(y-x\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left(y-x\right)\left[z\left(y+x\right)+xy\right]\)

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

2) \(xyz-\left(xy+yz+xz\right)+\left(x+y+z\right)-1\)

\(=xyz-xy-yz-xz+x+y+z-1\)

\(=\left(xyz-xy\right)-\left(yz-y\right)-\left(xz-x\right)+\left(z-1\right)\)

\(=xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(z-1\right)\)

\(=\left(z-1\right)\left(xy-y-x+1\right)\)

\(=\left(z-1\right)\left[\left(xy-y\right)-\left(x-1\right)\right]\)

\(=\left(z-1\right)\left[y\left(x-1\right)-\left(x-1\right)\right]\)

\(=\left(z-1\right)\left(x-1\right)\left(y-1\right)\)

\(a,-2x^3y^4-4x^4y^3+2x^3y^3\)

\(=-2x^3y^3\left(y+x-1\right)\)

\(b,ab\left(x-5\right)-a^2\left(5-x\right)\)

\(=\left(x-5\right)\left(ab+a^2\right)\)

tách nhỏ câu hỏi ra bạn

\(a.10x\left(x-y\right)-6y\left(y-x\right)\\ =10x\left(x-y\right)+6y\left(x-y\right)\\ =\left(10x-6y\right)\left(x-y\right)\\ =2\left(5x-3y\right)\left(x-y\right)\)

\(b.14x^2y-21xy^2+28x^3y^2\\ =7xy\left(x-y+xy\right)\)

\(c.x^2-4+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2+x-2\right)\\ =2x\left(x-2\right)\)

\(d.\left(x+1\right)^2-25\\ =\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

a,2x²-7x+6=(2x²-4x)-(3x-6)
=2x(x-3)-3(x-2)=(x-2)(2x-3)
b,x²+x-6=(x²+3x)-(2x+6)
=x(x-3)-2(x-3)=(x-3)(x-2)
c,x³+3x²+6x+4=x³+x²+2x²+2x+4x+4
=(x+1)(x²+2x+4)
d,x¹⁰+x⁵+1=(x¹⁰-x)+(x⁵-x²)+(x²+x+1)
=x((x³)³-1)+x²(x³-1)+(x²+x+1)
=x(x³-1)(x⁶+x³+1)+x²(x-1)(x²+x+1)+(x²+x+1)
=x(x-1)(x²+x+1)+x²(x-1)(x²+x+1)+(x²+x+1)
(x²+x+1)(x²-x+x³-x²+1)
e,(12x²-12xy+3y²)-10x(2x-y)=3(4x²-4xy+y²)-10x(2x-y)
=3(2x-y)²-10x(2x-y)=(2x-y)(6x-3y-10x)=(2x-y)(-4x-3y)

phân tích đa thức thành nhân tử

a,2x^2-7x+6
b,x^2+x-6
c,x^3+3x^2+6x+4
d,x^10+x^5+1
e,(12x^2-12xy+3y^2)-10x(2x-y)

\(2x^2-7x+6\)

\(=2x^2-3x-4x+6\)

\(=x\left(2x-3\right)-2\left(2x-3\right)\)

\(=\left(x-2\right)\left(2x-3\right)\)

           Bài làm :

 \(\text{a)}9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)

\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)

\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)

\(=\left(-x-3y-5\right)\left(7x+9y-1\right)\)

 \(\text{b)}3x^4y^2+3x^3y^2+3xy^2+3y^2\)

\(=\left(3x^4y^2+3xy^2\right)+\left(3x^3y^2+3y^2\right)\)

\(=3xy^2\left(x^3+1\right)+3y^2\left(x^3+1\right)\)

\(=\left(3xy^2+3y^2\right)\left(x^3+1\right)\)

\(=3y^2\left(x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)

\(=3y^2\left(x+1\right)^2\left(x^2-x+1\right)\)

 \(\text{c)}\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)

\(=\left(x+y-1\right)\left(x^2+x+y^2+y+1-xy\right)\)

\(d ) x^3+3x^2+3x+1-27z^3\)

\(=\left(x+1\right)^3-\left(3z\right)^3\)

\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)