Math, asked by Anonymous, 4 months ago

Without actually calculating the cubes, find the value of each of the following:-

 {( - 12)}^{3}  +  {(7)}^{3}  +  {(5)}^{3}

Answers

Answered by Anonymous
5

Step-by-step explanation:

 { (- 12)}^{3}  +  {(7)}^{3}  +  {(5)}^{3}

we \:  \:  \: can \:  \:  \: use \:  \:  \: the \:  \:  \: identity \:

{a}^{3}  +  {b}^{3}  +  {c}^{3}  = (a + b + c)( {a}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ac) + 3abc

 {( - 12)}^{3}  +  {(7)}^{3}  +  {(5)}^{3}  = ( - 12 + 7 + 5)( {( - 12)}^{2}  +  {(7)}^{2}  +  {(5)}^{2}  - ( - 12)(7) - (7)(5) - (5)( - 12)) + 3( - 12)(7)(5)

 = (0)(144 + 49 + 25 - 84 - 35 - 60) + 3( - 420)

 = (0)(39) + 3( - 420)

 = 0 + ( - 1260)

 =  - 1260

Answered by HARSHIT123RAJ
2

Answer:

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Step-by-step explanation:

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