a) y² + 2y = y(y + 2)

b) y³ - 2y² + y = y(y² - 2y + 1) = y(y - 1)²

c) y² - x² - 6y - 6x 

= (y + x)(y - x) - 6(y + x)

<=> (x + y)( y - x - 6)

d) x³ - 3x = x(x² - 3)

e) 2x - xy + 2z - yz 

= x(2 - y) + z(2 - y)

= (2 - y)(x + z)

Bài làm:

1) Ta có: \(2x^2+5xy+2y^2\)

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

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

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

2) Ta có: \(2x^2+2xy-4y^2\)

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

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

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

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

Làm tính nhân

(4x³+3xy²-2y³).(3x²-5xy-6y²)

=12x⁵+12y⁵-20x⁴y-36x²y³-8xy⁴

Phân tích đa thức thành nhân tử

10x³+5x²y-10x²y-10xy²+5y³

=10x³-5x²y-10xy²+5y³

=5(2x³-x²y-2xy²+y³-)

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

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

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

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