[tex]1)4 {x}^{2} (x + 2) - 12x(x + 2) + 9(x + 2)[/tex]
[tex] = (x + 2)(4 {x}^{2} - 12x + 9)[/tex]
[tex] = (x + 2)[ {(2x)}^{2} - 2 \times 2x \times 3 + {3}^{2} ][/tex]
[tex] = (x + 2) {(2x - 3)}^{2} [/tex]
[tex]2)4{x}^{3}(2x-1)-4{x}^{2}(2x-1)+2{x}^{2}-x[/tex]
[tex]=4{x}^{3}(2x-1)-4{x}^{2}(2x-1)+x(2x-1)[/tex]
[tex]=(2x-1)(4{x}^{3}-4{x}^{2}+x)[/tex]
[tex]=(2x-1)[x(4{x}^{2}-4x+1)][/tex]
[tex]=x(2x-1)[{(2x)}^{2}-2\times2x\times1+{1}^{2}][/tex]
[tex]=x(2x-1){(2x-1)}^{2}[/tex]
[tex]3)9{x}^{3}(3x+1)+6{x}^{2}(3x+1)+3{x}^{2}+x[/tex]
[tex]=9{x}^{3}(3x+1)+6{x}^{2}(3x+1)+x(3x+1)[/tex]
[tex]=(3x+1)(9{x}^{3}+6{x}^{2}+x)[/tex]
[tex]=(3x+1)[x(9{x}^{2}+6x+1)][/tex]
[tex]=x(3x+1)[{(3x)}^{2}+2\times3x\times1+{1}^{2}][/tex]
[tex]=x(3x+1){(3x+1)}^{2}[/tex]
[tex]=x{(3x+1)}^{3}[/tex]
