Question

evalute (104) cube and (999)cube​

Answer 1

$(i)$ $({104})^{3}$

$\:\sf\underline\red{We\:have}\:$

⠀⠀⠀⠀⠀⠀⠀$({104})^{3}$ = $({100+4})^{3}$

By using identity :-

⠀⠀= $({x+y}^{3})$ $=$ ${x}^{3}$ $+$ ${y}^{3}$ ${+}$ $3xy(x+y)$

⠀⠀⠀⠀= $({100})^{3}$ + $({4})^{3}$ + $3(100)(4)(100+4)$

⠀⠀⠀⠀= $1000000$ + $64$ + $124800$

⠀⠀⠀⠀${\pink{\boxed{\large{\bold{=\:1124864}}}}}$

$(i)$ $({999})^{3}$

$\:\sf\underline\orange{We\:have}\:$

⠀⠀⠀⠀⠀⠀⠀$({999})^{3}$ = $({1000-1})^{3}$

By using identity :-

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

⠀⠀⠀⠀⠀= $1000000000$ - $1$ - $2997000$⠀

⠀⠀⠀⠀⠀${\blue{\boxed{\large{\bold{=\:997002999}}}}}$⠀