Question

C%3A%20%20is%20%20%5C%3A%20doubled%20%20%5C%3A%20then%20%20%5C%3A%20%20%E2%80%8B%7D" id="TexFormula1" title=" \sf{prove \: that \: if \: a \: number \: is \: doubled \: then \: ​}" alt=" \sf{prove \: that \: if \: a \: number \: is \: doubled \: then \: ​}" align="absmiddle" class="latex-formula">
$\sf{its \: cube \: is \: 8 \: times \: the \: cube \: of \: the \: given \: number}$
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Answer 1

$\underline{\Large\underline\frak {\underline\red{Given:-} }}$

A number is doubled then it's Cube is 8 times.

$\underline{\Large\underline\frak {\underline\orange{Vube \:figure } } :- }$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} {\begin{gathered} \sf{ } \: \: \: \huge\boxed{ \begin{array}{cc} \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \: } \end{gathered}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\underline{\Large\underline\frak {\underline\purple{ Formula \:used \: \: } : }} \\ \\ \sf \: \blue{\underline{\boxed{ \sf \: a \times a \times a = {a}^{3} }}}\end{gathered}$

$\bf \: Now\bf \: according \: to \: Question :-$

$\begin{gathered} \sf \: double \: of \: cube \: = 2 + a \\ \\ \sf \qquad \qquad \: \: \: \: \: \: \: = 2a\end{gathered}$

$\begin{gathered} \sf \: let \: a \: number \: be \: = a \\ \\ \sf \: it's \: cube \: will \: be \: = a \times a \times a = {a}^{3} \\ \end{gathered}$

$\sf \pink{ = 2a \times 2a \times 2a = 8 {a}^{2} \: or \: {(2a)}^{3}}$

Hence, Proved that double 8 times the cube of a number = 8 times the cube of number a = 8 × a³ = 8 × x³

$\bf \green{R.H.S. = L.H.S.}$

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Answer 2

let a number = a

it's cube will be a×a×a = a³

now atq 2a

it's cube will be

2a ×2a ×2a => 8a³ or (2a)³

Hope it helps you