a) \(2x^2+5x+2\)

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

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

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

b) \(4x^2-4x-9y^2+12y-3\)

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

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

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

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

c) \(x^4-2x^3-4x^2+4x-3\)

\(=x^4+x^3-x^2+x-3x^2-3x+3x-3\)

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

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

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

d) \(x^3-x+3x^2y+3xy^2+y^3-y\)

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

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

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

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

Lời giải:

$2x^2+3x-5=(2x^2-2x)+(5x-5)=2x(x-1)+5(x-1)=(x-1)(2x+5)$

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

Hãy cho em lời giải trước 4h 

\(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2\right)-8x\left(x-y\right)=2x\left(x-y\right)\left(x+y\right)-8x\left(x-y\right)=2x\left(x-y\right)\left(x+y-4\right)\)

\(2x^3-2xy^2-8x^2+8xy\)

\(=2x\left(x^2-y^2\right)-8x\left(x-y\right)\)

\(=2x\left(x+y\right)\left(x-y\right)-8x\left(x-y\right)\)

\(=\left[2x\left(x+y\right)-8x\right]\left(x-y\right)\)

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

\(2x^3-2xy^2-8x^2+8xy\)

\(=2x\left(x^2-y^2\right)-8x\left(x-y\right)\)

\(=\left(x-y\right)\left[2x\left(x+y\right)-8x\right]\)

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

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

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

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

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

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

Bạn xem lại đề

a. 5x³-10x²+5x

= 5x(x²-2x+1)

= 5x(x-1)²