Question

If x = -2, y = 3, z = 1, then the value of ${x^3} + {y^3} + {z^3} - 3xyz$ is:
A.38
B.37
C.-37
D.-38

Answer 1

Hint: We are required to calculate the value of the given equation with values of variables provided. We will just put the values provided in the given equation.

Complete step by step Answer:
We are given the values of the variables as x = - 2, y = 3, z = 1.
Substituting the values of the variables in ${x^3} + {y^3} + {z^3} - 3xyz$, we get:
$(- 2)^3 + (3)^3 + (1)^3$ – 3 (- 2) (3) (1) = - 8 + 27 + 1 + 18 = 38
$ \Rightarrow $${x^3} + {y^3} + {z^3} - 3xyz$ = 38
Therefore, option(a) is correct.

Note: In such questions, we need not to waste our time thinking what to proceed with. Merely putting the values provided in the given equation will do the needful. You may get confused thinking this problem is tough but it is as simple as it seems.

Additional Information: We used an algebraic identity in the above mentioned question. We can define the algebraic identities as an equality which holds for each and every value of its variables is called an algebraic identity or an identity is an equality relating one mathematical expression with the other.
In other words, we can say that an algebraic identity is basically an equality in which every value of its variables holds true.
Muhammad ibn Musa al - Khwarizmi, the father of algebra, derived these identities in his book, Kitab – al – jabr.