x² + 2xy + y² - 9z²

=(x + y)² - 9z²

= (x + y - 3z)(x + y + 3z)

Ta có: \(x^2+2xy+y^2-9z^2=\) \(\left(x+y\right)^2-\left(3z\right)^2\)

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

a) \(x^2-xy+x-y\)

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

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

b) \(x^2+5x+6\)

\(=x^2+2x+3x+6\)

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

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

\(2xy-x^2-y^2+16\)

\(=16-\left(x-y\right)^2\)

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

a)

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

b)

\(x^2-2xy+y^2-16\\ =\left(x^2-2xy+y^2\right)-16\\ =\left(x-y\right)^2-16\\ =\left(x-y-4\right)\left(x-y+4\right)\)

a) x³-2x²-x+2

=x(x²-1)+2(-x²+1)

=x(x²-1)-2(x²-1)

=(x²-1)(x-2)

b)

x²+6x-y²+9

=x²+6x+9-y²

=(x+3)²-y²

^{=(x+3-y)(x+3+y)}

a)x^2-4xy+4y^2-4

=(x²-4xy+4y²)-4

=(x-2y)²-4

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

b)16-x^2+2xy-y^2

=16-(x²-2xy+y²)

=16-(x-y)²

=[4-(x-y)][4+(x-y)]

=(4-x+y)(4+x-y)

\(2xy-x^2-y^2+16\)

\(=-\left(x^2-2xy+y^2-16\right)\)

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

\(=-\left[\left(x-y\right)^2-4^2\right]\)

\(=-\left[\left(x-y-4\right)\left(x-y+4\right)\right]\)

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

\(=16-\left(x^2-2xy+y^2\right)\)

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

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

x\(^2\)-2xy+y\(^2\)-6x+6y

=(x-y)\(^2\)-6(x+y)

=-6(x+y)+(x-y)\(^2\)

\(x^2-2xy+y^2-6x+6y=\left(x-y\right)^2-6\left(x-y\right)=\left(x-y\right)\left(x-y-6\right)\)

x^2-2xy+y^2-6x+6y

=(x-y)^2-6(x-y)

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