Question

What is the
Formula of x3+y3+z3

Answer 1

Given :

x³ + y³ + z³

To Find :

The Formula for x³ + y³ + z³

Solution :

The Formula for x³ + y³ + z³ can be derived from the formula of  x³ + y³ + z³ - 3xyz.

We know,

            x³ + y³ + z³ - 3xyz =  (x+ y + z) (x² + y² + z² – xy – yz– zx)

In order to find the formula of x³ + y³ + z³, we need to send -3xyz to the right side of equal sign.

Thus the formula becomes,

x³ + y³ + z³ = (x+ y + z) (x² + y² + z² – xy – yz– zx) + 3xyz

Answer 2

Answer:

Step-by-step explanation:

Disclaimer:

What is the Formula of $x^{3} +y^{3} +z^{3}$ ?

Concept:

The concept of alzebra will be used to solve this question.To solve an algebraic problem, we replace the numbers with letters or alphabets. In order to represent unknown numbers in an equation, we utilise letters like ($x, a, b,$ etc.). The algebraic formula is then solved to yield a clear solution.

Given:

The expression of the question is  $x^{3} +y^{3} +z^{3}$ .

To find:

We need to find the formula of this expression.

Solution:

The formula can be derived from $x^{3} +y^{3} +z^{3}-3xyz$ - this expression.

The formula is

$x^{3} +y^{3} +z^{3}-3xyz= (x+y+z)\left(x^{2}+y^{2}+z^{2}-x y-y z-z x\right)$

Here we need to find only the formula of $x^{3} +y^{3} +z^{3}$ .

So $-3xyz$ will be sent to the RHS.

Now the final formula is $x^{3} +y^{3} +z^{3}= (x+y+z)\left(x^{2}+y^{2}+z^{2}-x y-y z-z x\right) +3xyz$ .

The answer is $(x+y+z)\left(x^{2}+y^{2}+z^{2}-x y-y z-z x\right) +3xyz$ .

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