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

\(x^2-9+5xy-15y=\left(x-3\right)\left(x+3\right)+5y\left(x-3\right)=\left(x-3\right)\left(x+3+5y\right)\)

\(a,=4\left(x-5y\right)\\ b,=5x\left(x+y\right)-\left(x+y\right)=\left(5x-1\right)\left(x+y\right)\\ c,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

a) 4x - 20y

= 4 ( x - 5y )

b) 5x^2 + 5xy - x - y

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

= ( x + y ) ( 5x - 1 )

c) x^2 - 2xy - z^2 + y^2

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

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

= ( x - y + z ) ( x - y - z )

a) \(4\left(x-5y\right)\)

b) \(5x^2+5xy-x-y\)

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

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

c) \(x^2-2xy-z^2+y^2\)

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

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

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

\(5x^2+5xy-x-y\)

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

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

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

`5x^2 + 5xy +x +y`

`=(5x^2 + 5xy )+(x+y)`

`=5x(x+y)+(x+y)`

`=(x+y)(5x+1)`

 5\(x^2\)+5xy+x+y = (5\(x^2\)+x)+(5xy+y)

                       = x(5x+1)+y(5x+1)

                       = (5x+1)(x+y)

a: =5x(x-y)-7(x-y)

=(x-y)(5x-7)

b: =x(x+2y)+(x+2y)

=(x+2y)(x+1)

c; =(x-3)^2-9y^2

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

a

\(5x^2-5xy+7y-7x\\ =5x\left(x-y\right)+7\left(y-x\right)\\ =5x\left(x-y\right)-7\left(x-y\right)\\ =\left(5x-7\right)\left(x-y\right)\)

b

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

c

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

\(a,a^4+a^2+1\)

\(=\left(a^2\right)^2+2a^2+1-a^2\)

\(=\left(a^2+1\right)^2-a^2\)

\(=\left(a^2+1-a\right)\left(a^2+1+a\right)\)

\(---\)

\(b,a^4+a^2-2\)

\(=a^4-a^2+2a^2-2\)

\(=a^2\left(a^2-1\right)+2\left(a^2-1\right)\)

\(=\left(a^2-1\right)\left(a^2+2\right)\)

\(=\left(a-1\right)\left(a+1\right)\left(a^2+2\right)\)

\(---\)

\(c,x^3-5x^2-14x\)

\(=x^3+2x^2-7x^2-14x\)

\(=x^2\left(x+2\right)-7x\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-7x\right)\)

\(=x\left(x+2\right)\left(x-7\right)\)

\(a.a^4+a^2+1\) 

\(=\left(a^4+2a^2+1\right)-a^2\) 

\(=\left(a^2+1\right)^2-a^2\)  

\(=\left(a^2+1+a\right)\left(a^2+1-a\right)\) 

\(b.a^4+a^2-2\) 

\(=a^4+2a^2-a^2-2\) 

\(=a^2\left(a^2+2\right)-\left(a^2-2\right)\) 

\(=\left(a^2+2\right)\left(a^2-1\right)\) 

\(=\left(a^2+2\right)\left(a-1\right)\left(a+1\right)\) 

\(c.x^3-5x^2-14x\) 

\(=x^3+2x^2-7x^2-14\) 

\(=x^3\left(x+2\right)-7x\left(x+2\right)\) 

\(=\left(x^3-7x\right)\left(x+2\right)\) 

\(=x\left(x-7x\right)\left(x+2\right)\) 

\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+xy^2+xyz\right)+\left(y^2z+yz^2+xyz\right)+\left(x^2z+xz^2+xyz\right)\)

\(=xy\left(x+y+z\right)+yz\left(y+z+x\right)+xz\left(x+z+y\right)\)

\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)

a: Ta có: \(x^2-xy-3x+3y\)

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

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

b: Ta có: \(5x^2+5xy-x-y\)

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

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

c: Ta có: \(x^2-2xy+y^2-z^2\)

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

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

a) \(x^2+5x+5xy+25y\)

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

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

c) \(x^2-24x-25\)

\(=x^2-25x+x-25\)

\(=x\left(x-25\right)+\left(x-25\right)\)

\(\left(x+1\right)\left(x-25\right)\)