Question

Without actually calculating the cubes, find the value of (-23)^3 + 15^3 + 8^3

Answer 1

Step-by-step explanation:

your solution dear....

Answer 2

The value of the given expression without actually calculating the cubes is -8280.

We need to evaluate the given cubic expression without solving the cubes. So, we use the sum of cube identity here.

Identity for cubes in 3 variables :

There is an identity for the cube of three variables 'a', 'b', 'c' as :

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

Here, in the given expression we have :

• a = -23
• b = 15
• c = 8

Evaluating the RHS of the identity :

     $RHS = (a+b+c)(a^{2} +b^{2} +c^{2} -ab-bc-ac) \\RHS = (-23+15+8)((-23)^{2} +15^{2} +8^{2} -(-23)(15)-(15)(8)-(-23)(8) \\RHS = (-23+23)((-23)^{2} +15^{2} +8^{2} -(-23)(15)-(15)(8)-(-23)(8) \\RHS = 0 * ((-23)^{2} +15^{2} +8^{2} -(-23)(15)-(15)(8)-(-23)(8)) \\RHS = 0$

     

So, the special case of the identity is that when the sum of the three variables is 0, the RHS becomes 0.

             $a^{3} +b^{3} +c^{3} - 3abc = 0\\a^{3} +b^{3} +c^{3} = 3abc$

So, here the sum of the given cube values can be directly calculated as the special case of the cube identity as ( -23 + 15 + 8 = 0 ) :

            $(-23)^{3} +15^{3} +8^{3} = 3(-23)(15)(8)$

                                         $= -23 * 15 * 8$

                                          $= -8280$

Hence, the value of the given expression is -8280.

To learn more about Cubic Identities, visit

https://brainly.in/question/14041307

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