\(=\left(x^7+x^6+x^5-x^3-x^2\right)-\left(x^6+x^5+x^4-x^2-x\right)+\left(x^5+x^4+x^3-x-1\right)\)

\(=x^2\left(x^5+x^4+x^3-x^2-1\right)-x\left(x^5+x^4+x^3-x-1\right)+\left(x^5+x^4+x^3-x-1\right)\)

\(=\left(x^2-x+1\right)\left(x^5+x^4+x^3-x^2-1\right)\)

\(x\cdot\left(x+1\right)\cdot\left(x+2\right)\cdot\left(x+3\right)+1\)

\(=\left(x+1\right)\left(x+2\right)\left[x\left(x+3\right)\right]+1\)

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

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

gọi \(\left(x^2+3x\right)=a\)

\(\Rightarrow\left(t+2\right)t+1\)

\(=t^2+2t+1=\left(t+1\right)^2\)

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

\(\Rightarrow x\cdot\left(x+1\right)\cdot\left(x+2\right)\cdot\left(x+3\right)+1\)\(=\left(x^2+3x+1\right)^2\)

\(5x^2y^2-30xy^2+5xy=5xy\left(xy-6y+1\right)\)

\(5x^2y^2-30xy^2+5xy=5xy\left(xy-6y+1\right)\)

\(1,12x^2y-27y^3=3y\left(4x^2-9y^2\right)=3y\left(2x+3y\right)\left(2x-3y\right)\\ 2,4x^2-36=4\left(x^2-9\right)=4\left(x-3\right)\left(x+3\right)\\ 3,x^2-4x+4-y^2=\left(x-2\right)^2-y^2=\left(x-y-2\right)\left(x+y-2\right)\\ 4,\left(3x+1\right)^2-\left(x-2\right)^2=\left(3x+1-x+2\right)\left(3x+1+x-2\right)=\left(2x+3\right)\left(4x-1\right)\)

\(1,=3y\left(4x^2-9y^2\right)=3y\left(2x+3y\right)\left(2x-3y\right)\)

\(2,=4\left(x^2-9\right)=4\left(x-3\right)\left(x+3\right)\)

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

\(4,=\left(3x+1-x+2\right)\left(3x+1+x-2\right)=\left(2x+3\right)\left(4x-1\right)\)

Đề sai nhé .Sửu lại

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

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

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

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