1)

[tex]6 {a}^{3} - 6a[/tex]

[tex]6a( {a}^{2} - 1)[/tex]

[tex]6a(a + 1)(a - 1)[/tex]

2)

[tex]2 {x}^{2} + 24xy + 72 {y}^{2} [/tex]

[tex]2( {x}^{2} + 12xy + 36 {y}^{2} )[/tex]

[tex]2(x + 6y)(x + 6y)[/tex]

[tex]2 {(x + 6y)}^{2} [/tex]

3)

[tex] {a}^{2} - ab - {a}^{2} b + {a}^{2} [/tex]

[tex]a( {a}^{2} - b - ab + a)[/tex]

[tex]a(a - b)(a + 1)[/tex]

4)

[tex] {x}^{2} - 2xy + {y}^{2} - 49[/tex]

[tex] {(x - y)}^{2} - 49[/tex]

[tex] {(x - y)}^{2} - {7}^{2} [/tex]

[tex]((x - y) + 7)((x - y) - 7)[/tex]

[tex]( x - y + 7)(x - y - 7)[/tex]

5)

[tex] {a}^{3} + 8 - {a}^{2} - 2a[/tex]

[tex] {a}^{3} - {a}^{2} - 2a + 8[/tex]

[tex](a + 2) \frac{ {a}^{3} - {a}^{2} - 2a + 8 }{a + 2} [/tex]

[tex](a + 2)( {a}^{2} - 3a + 4)[/tex]

6)

[tex] {m}^{3} + 27 {n}^{3} + {m}^{2} + 6mn + 9 {n}^{2} [/tex]

[tex] {m}^{2} + 27 {n}^{2} + {m}^{2} + 6mn + 9 {n}^{2} [/tex]