a) x³-2x²-x+2

=x(x²-1)+2(-x²+1)

=x(x²-1)-2(x²-1)

=(x²-1)(x-2)

b)

x²+6x-y²+9

=x²+6x+9-y²

=(x+3)²-y²

^{=(x+3-y)(x+3+y)}

x³-5x²+2x+8

=x³-6x²+8x+x²-6x+8

=x(x²-6x+8)+(x²-6x+8)

=(x²-6x+8)(x+1)

=[x²-2x-4x+8](x+1)

=[x(x-2)-4(x-2)](x+1)

=(x-4)(x-2)(x+1)

tích đúng mình giải cho

a) 1/2(x³+8)=1/2(x+2)(x²-2x+4)

b) x⁴(x-y)+2x³(x-y)=x³(x+2)(x-y)

c) x²-(y²-6y+9)=x²-(y-3)²=(x-y+3)(x+y-3)

d) xy(x³+y³)=xy(x+y)(x²-xy+y²)

e)3x²(x²-25y²)=3x²(x-5y)(x+5y)

f) 4x⁴+4x²y²+y⁴-4x²y²= (2x²+y²)²-(2xy)²=(2x²-2xy+y²)(2x²+2xy+y²)

a) \(\frac{1}{2}x^3+4=\frac{1}{2}\left(x^3+8\right)=\frac{1}{2}\left(x+2\right)\left(x^2-2x+4\right)\)

b) \(x^5-x^4y+2x^4-2x^3y=x^3\left(x^2-xy+2x-2y\right)=x^3\left[x\left(x-y\right)+2\left(x-y\right)\right]=x^2\left(x-y\right)\left(x+2\right)\)

c) \(x^2-y^2+6y-9=x^2-\left(y-3\right)^2=\left(x+y-3\right)\left(x-y+3\right)\)

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

e) \(3x^4-75x^2y^2=3x^2\left(x^2-25y^2\right)=3x^2\left(x+5y\right)\left(x-5y\right)\).

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

a: =(x+y)(x-3)

b: =x(x^2-2x+1+4y^2)

a) \(x^2-x-xy-2y^2+2y\)

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

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

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

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

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

b) \(x^2+4xy+2x+3y^2+6y\)

\(=x^2+3xy+xy+2x+3y^2+6y\)

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

\(=3y\left(y+x+2\right)+x\left(y+x+2\right)\)

\(=\left(3y+x\right)\left(y+x+2\right)\)