Step-by-step explanation:
[tex] \underline{ \underline{ \text{Solution}}} : [/tex]
[tex] \text{1. \: First \: expression} : \tt{2 {x}^{4} - 6 {x}^{3} - 8 {x}^{2} }[/tex]
⤑ [tex] \tt{2 {x}^{2}( {x}^{2} - 3x - 4) }[/tex]
⤑ [tex] \tt{2 {x}^{2} \{ \: {x}^{2 } - \: (4 - 1)x - 4 \} }[/tex]
⤑ [tex] \tt{2 {x}^{2} \{ {x}^{2} - 4x + x - 4 \} }[/tex]
⤑ [tex] \tt{2 {x}^{2} \{ x(x - 4) + 1(x - 4) \} }[/tex]
⤑ [tex] \tt{2 {x}^{2} (x - 4)(x + 1)}[/tex]
[tex] \text{2. Second \: expression} : \tt{4 {x}^{3} - 4x }[/tex]
⤑ [tex] \tt{4x( {x}^{2} - 1)}[/tex]
⤑ [tex] \tt{4x(x + 1)(x - 1)}[/tex]
L.C.M = Common × Remaining
= ( x + 1 ) × ( x - 1 ) × ( x - 4 ) × 2x² × 4x
= 8x³ ( x + 1 ) ( x - 1 ) ( x - 4 )
[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt \: 8 {x}^{3} (x + 1)(x - 1)(x - 4)}}}}}}[/tex]
Hope I helped !
Have a wonderful day / night !
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