Ta có:\(x^3-2x^2-9xy^2+x\)

\(=x\left(x^2-2x-9y^2+1\right)=x\left(x^2-2x+1-9y^2\right)\)

\(=x\left[\left(x-1\right)^2-9y^2\right]=x\left(x-3y-1\right)\left(x-1+3y\right)\)

a: =x(4x^2+4x+1)

=x(2x+1)^2

b: =(x-y)^2-49

=(x-y-7)(x-y+7)

Câu 1:

\(4x^2+16x-9\)

\(=4x^2+18x-2x-9\)

\(=2x\left(2x+9\right)-\left(2x+9\right)\)

\(=\left(2x-1\right)\left(2x+9\right)\)

Câu 2:

\(6x^2-11x+3=0\)

\(\Leftrightarrow6x^2-2x-9x+3=0\)

\(\Leftrightarrow2x\left(3x-1\right)-3\left(3x-1\right)=0\)

\(\Leftrightarrow\left(2x-3\right)\left(3x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=3\\3x=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)

b) Ta có: \(x^3-x^2y-xy^2+y^3\)

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

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

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

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

c: \(x^2-4+3\left(x-2\right)^2\)

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

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

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

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

a,x^2-x-y^2-y

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

=(x-y).(x+y)-(x+y)

=(x+y).(x-y-1)

b, x^2-2xy+y^2-z^2

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

=(x-y)^2-z^2

=(x-y-z)(x-y+z)

c,5x-5y+ax-ay( đề bài ở đây phải là -ay ms tính đc)

=(5x-5y)+(ax-ay)

=5(x-y)+a(x-y)

=(x-y).(5+a)

d,a^3-a^2.x-ay+xy

=(a^3-a^2x)-(ay-xy)

=a^2(a-x)-y(a-x)

=(a-x)(a^2-y)

e,4x^2-y^2+4x+1

={(2x)^2+4x+1}-y^2

=(2x+1)^2-y^2

=(2x+1+y^2)(2x+1-y^2)

f,x^3-x+y^3-y

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

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

=(x+y)(x^2-xy+y^2-1)

\(a,x^2+6x+9\)

\(=x^2+3x+3x+9\)

\(=\left(x^2+3x\right)+\left(3x+9\right)\)

\(=x.\left(x+3\right)+3.\left(x+3\right)\)

\(=\left(x+3\right).\left(x+3\right)\)

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

\(b,10x-25-x^2\)

\(=-\left(x^2-2.5.x+5^2\right)\)

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

\(c,x^2+4x-y^2+4\)

\(=\left(x^2+2.2.x+2^2\right)-y^2\)

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

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

\(d,3x^2+6xy+3y^2-3z^2\)

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

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

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

\(e,x^2-2xy+y^2-z^2+2zt-t^2\)

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

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

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

\(=\left(x-y-z+t\right).\left(x-y+z-t\right)\)

bai tim x bai 5 co 

\(x^6+6x+9\)

\(=x^2+2.x.3+3^2\)

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

hk tốt

^^

HAHA :) 4 năm vẫn chưa có ai trả lời, nhục !