[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
- Firstly , You'll have to know the formula of a³ - b³ i.e a³ - b³ = ( a - b ) ( a² + ab + b² )
- What's the cube root of 1000 ? - It's 10 ! How ?
- [tex] \sqrt[3]{1000} = \sqrt[3]{ \underline{10} \times \underline{ 1 0} \times \underline{ 10} } = \boxed{10}[/tex]
[tex] \large{ \tt{❁ \: LET'S\: START}} : [/tex]
[tex] \large{ \bf{ ❀ \: \ {x}^{3 } - 1000}}[/tex]
- Write the number into the exponential form with the exponent 3 :
[tex] \large{ \bf{↦ {x}^{3} - {10}^{3} }}[/tex]
- Here , Suppose ' x ' as ' a ' & ' 10 ' as ' b '. Use the formula of a³ - b³ :
[tex]↦{ \large{ \bf{(x - 10)( {x}^{2} + x \times 10 + {10}^{2} }}})[/tex]
[tex]↦ \boxed{\large{ \bf{(x - 10)( {x}^{2} + 10x + 100) }}}[/tex]
- Hence , Second option is the correct choice !
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ツ Hope I helped! ۵
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