Question

4xla2(×+2)-12×(×+2)+9(×+2)​

Answer 1

$1)4 {x}^{2} (x + 2) - 12x(x + 2) + 9(x + 2)$

$= (x + 2)(4 {x}^{2} - 12x + 9)$

$= (x + 2)[ {(2x)}^{2} - 2 \times 2x \times 3 + {3}^{2} ]$

$= (x + 2) {(2x - 3)}^{2}$

$2)4{x}^{3}(2x-1)-4{x}^{2}(2x-1)+2{x}^{2}-x$

$=4{x}^{3}(2x-1)-4{x}^{2}(2x-1)+x(2x-1)$

$=(2x-1)(4{x}^{3}-4{x}^{2}+x)$

$=(2x-1)[x(4{x}^{2}-4x+1)]$

$=x(2x-1)[{(2x)}^{2}-2\times2x\times1+{1}^{2}]$

$=x(2x-1){(2x-1)}^{2}$

$3)9{x}^{3}(3x+1)+6{x}^{2}(3x+1)+3{x}^{2}+x$

$=9{x}^{3}(3x+1)+6{x}^{2}(3x+1)+x(3x+1)$

$=(3x+1)(9{x}^{3}+6{x}^{2}+x)$

$=(3x+1)[x(9{x}^{2}+6x+1)]$

$=x(3x+1)[{(3x)}^{2}+2\times3x\times1+{1}^{2}]$

$=x(3x+1){(3x+1)}^{2}$

$=x{(3x+1)}^{3}$