Question

Phân tích đa thức thành nhân tử:

(5x - 2y)(5x + 2y) + 4y - 1

x^2(xy + 1) + 2y - x - 3xy

Answer 1

\(\left(5x-2y\right)\left(5x+2y\right)+4y-1=25x^2-4y^2+4y-1\)

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

\(=\left(5x-2y+1\right)\left(5y+2y-1\right)\)

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

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

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