a, -x - y² + x² - y = (x² - y²) - (x + y)

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

= (x + y)(x - y - 1)

b, x( x + y ) - 5x - 5y = x(x + y) - 5(x + y)

= (x - 5)(x + y)
c, x² - 5x + 5y - y² = (x - y)(x + y) - 5(x - y)

= (x - y)(x + y - 5)
d, 5x³ - 5x²y - 10x² + 10xy = 5x²(x - y) - 10x(x - y)

= 5x(x - y)(x - 2)
e, 27x³ - 8y³ = (3x - 2y)(9x² + 6xy + 4y²)
f, x² - y² - x - y = (x - y)(x + y) - (x + y)

= (x + y)(x - y - 1)
g, x² - y² - 2xy + y² = (x² - 2xy + y²) - y²

= (x - y)² - y²

= (x - y - y)(x - y + y) = x(x - 2y)
h, x² - y² + 4 - 4x = (x² - 4x + 4) - y²

= (x - 2)² - y²

= (x - y - 2)(x + y - 2)
i, x³ + 3x² + 3x + 1 - 27z³ = (x + 1)³ - 27z³

= (x+1-3z)(x²+2x+1+3xz+3z+9z²)
k, 4x² + 4x - 9y² + 1 = (2x + 1)² - 9y²

= (2x - 3y + 1)(2x + 3y + 1)
m, x² - 3x + xy - 3y = x(x - 3) + y(x - 3)

= (x - 3)(x + y)

a) \(x^4+4x^2-5=x^4+4x^2+4-9=\left(x^2+2\right)^2-3^2\)

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

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

c) \(x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)

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

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

e) \(5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)\)

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

f) \(27x^3-8y^3=\left(3x\right)^3-\left(2y\right)^3=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

\(a,14x^2y-21xy^2+28x^2y^2=7xy\left(x-3y+4xy\right)\\ b,x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\\ c,10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x+8\right)=2\left(x-y\right)\left(5x+4\right)\)

\(d,\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)\(e,x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

a: \(5x-20y=5\left(x-4y\right)\)

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

c: \(x\left(x+y\right)-\left(5x+5y\right)=\left(x+y\right)\left(x-5\right)\)

d: \(5\left(x-y\right)+y\left(x-y\right)=\left(x-y\right)\left(y+5\right)\)

\(1,=\left(x-3\right)\left(x+3\right)\\ 2,=\left(x-y\right)\left(5+a\right)\\ 3,=\left(x+3\right)^2\\ 4,=\left(x-y\right)\left(10x+7y\right)\\ 5,=5\left(x-3y\right)\\ 6,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

bạn gõ lại công thức cho rõ đi, khó đọc quá

\(10x\left(x-y\right)-6y\left(y-x\right)\)

\(=10x\left(x-y\right)+6x\left(x-y\right)\)

\(=\left(10x+6x\right)\left(x-y\right)\)

\(c,3x^2+5y-3xy-5x\)

\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)

\(=3x\left(x-y\right)-5\left(x-y\right)\)

\(=\left(3x-5\right)\left(x-y\right)\)

\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)

\(f,8x^3-12x^2y+6xy^2-y^3\)

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

\(g,x^3+8y^3=x^3+\left(2y\right)^3\)

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

\(i,x^2-25-2xy+y^2\)

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

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