\(x-3\sqrt{x}+2=x-\sqrt{x}-2\sqrt{x}+2=\sqrt{x}\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)=\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)\)

\(x-3\sqrt{x}+2=\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)\)

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

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

=(3x-1)(5x+1)

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

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

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

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

------------------------------------

\(a^3+3a^2-6a-8\)

\(=a^3+4a^2-a^2-4a-2a-8\)

\(=\left(a^3+4a^2\right)-\left(a^2+4a\right)-\left(2a+8\right)\)

\(=a^2\left(a+4\right)-a\left(a+4\right)-2\left(a+4\right)\)

\(=\left(a+4\right)\left(a^2-a-2\right)\)

\(=\left(a+4\right)\left(a^2-2a+a-2\right)\)

\(=\left(a+4\right)\left[\left(a^2-2a\right)+\left(a-2\right)\right]\)

\(=\left(a+4\right)\left[a\left(a-2\right)+\left(a-2\right)\right]\)

\(=\left(a+4\right)\left(a-2\right)\left(a+1\right)\)

---------------------------------

\(2x^2-5x+2\)

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

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

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

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

-----------------------------------------

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

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

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

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

-------------------------------------

\(a^2-1+4b-4b^2\)

\(=a^2-\left(1-4b+4b^2\right)\)

\(=a^2-\left(1-2b\right)^2\)

\(=\left(a-1+2b\right)\left(a+1-2b\right)\)

----------------------------------------

\(a^4+6a^2b+9b^2-1\)

\(=\left(a^4+6a^2b+9b^2\right)-1\)

\(=\left(a^2+3b\right)^2-1\)

\(=\left(a^2+3b-1\right)\left(a^2+3b+1\right)\)

---------------------------------

\(2x^3+16y^3\)

\(=2\left(x^3+8y^3\right)\)

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

Lần sau ghi đề tách riêng từng câu ra nhé em. Ghi dính chùm vậy khó nhìn lắm. Sẽ ít ai giải cho em

−5𝑥^2−8𝑥+4

\(=\left[2\left(x-1\right)-3x\right]\left[2\left(x-1\right)+3x\right]\\ =\left(2x-2-3x\right)\left(2x-2+3x\right)\\ =\left(-2-x\right)\left(5x-2\right)\\ =\left(x+2\right)\left(2-5x\right)\)

\(4\left(x-1\right)^2-9x^2=\left(2x-2\right)^2-\left(3x\right)^2=\left(2x-2-3x\right)\left(2x-2+3x\right)=\left(-x-2\right)\left(5x-2\right)=-\left(x+2\right)\left(5x-2\right)=\left(x+2\right)\left(2-5x\right)\)

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

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

\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

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

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

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

b: \(=\left(x^2+1\right)^2+x\left(x^2+1\right)+2x\left(x^2+1\right)+2x^2\)

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

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

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

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