Question

Phân tích thành nhân tử :

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

b, \(x^2\cdot\left(1-x^2\right)-4-4x^2\)

c, \(x^3+2x^2+2x+1\)

d, \(x^4-2x^3+2x-1\)

Answer 1

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

\(=x^2-2x+1-4y^2-4y-1\)

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

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

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

b) Mình nghĩ câu này sai đề

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

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

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

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

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

d) \(x^4-2x^3+2x-1\)

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

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

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

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

Answer 2

a, (x-2y)(x+2y)-2(x+2y) = (x+2y)(x-2y-2)