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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Ta có: \(a^2b + a^2c + ab^2 + ac^2 + b^2c + bc^2 + 2abc\)

\(= a^2(b + c) + a(b^2 + 2bc + c^2) + bc(b + c)\)

\(= a^2(b + c) + a(b + c)^2 + bc(b + c)\)

\(= (b + c)\left[ a^2 + a(b + c) + bc \right]\)

\(= (b + c)\left[ a^2 + ab + ac + bc \right]\)

=(b+c)(a+b)(a+c)

x³+2x²+x

= x ( x\(^2\) + 2x + 1 )

= x ( x + 1 )\(^2\)

a.

\(x^3-y^3+2x^2-2y^2\)

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

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

b.

\(x^3+1-x^2-x\)

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

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

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

`(x+y)^3-x^3-y^3`

`=(x+y)^3-(x^3+y^3)`

`=(x+y)^3-(x+y)(x^2-xy+y^2)`

`=(x+y)[(x+y)^2-x^2+xy-y^2]`

`=(x+y)(x^2+2xy+y^2-x^2+xy-y^2)`

`=(x+y).3xy`

a) Ta có: \(\left(x+y\right)^3-x^3-y^3\)

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

\(=3xy\left(x+y\right)\)

\(a,=x\left(y^2-25\right)=x\left(y-5\right)\left(y+5\right)\\ b,=x\left(x-y\right)+2\left(x-y\right)=\left(x+2\right)\left(x-y\right)\\ c,=x^2\left(x-3\right)-4\left(x-3\right)\\ =\left(x-2\right)\left(x+2\right)\left(x-3\right)\)

a,x³-27+3x(x-3)

=(x-3)(x²+3x+9)+3x(x-3)

=(x-3)(x²+6x+9)

=(x-3)(x+3)²

b,5x³-7x²+10x-14

= x²(5x-7)+2(5x-7)

= (5x-7)(x²+2)

a,x³-27+3x(x-3)

=(x-3)(x²+3x+9)+3x(x-3)

=(x-3)(x²+3x+9+3x)

=(x-3)(x²+6x+9)

=(x-3)(x+3)²

b,5x³-7x²+10x-14

=(5x³+10x)-(7x²+14)

=5x(x²+2)-7(x²+2)

=(x²+2)(5x-7)