Question

Phân tích các đa thức sau thành nhân tử:

a,  x2 – 2x – 4y2 + 4y

b, x⁴ + 6x²y + 9y² – 1 

Answer 1

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

Answer 2

\(b)x^4+6x^2y+9y^2-1\\=(x^4+6x^2y+9y^2)-1\\=(x^2+3y)^2-1\\=(x^2+3y-1)(x^2+3y+1)\\a) x^2-2x+4y^2+4y\\=(x^2-4y^2)-(2x-4y)\\=(x-2y)(x+2y)-2(x-2y)\\=(x-2y)(x+2y-2)\)

Answer 3

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

\(x^4+6x^2y+9y^2-1=\left(x^2+3y\right)^2-1=\left(x^2+3y-1\right)\left(x^2+3y+1\right)\)