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If $x + y + z = 9$ and $x y + yz + z x = 26$ , find $x^{3} + y^{3} + z^{3} - 3 x yz$ .

Class 9Algebraic IdentitiesPolynomials

A27
B261
C−153
D9

Step-by-Step Solution

First

x^{2} + y^{2} + z^{2} = 81 - 52 = 29

. Then

x^{3} + y^{3} + z^{3} - 3 x yz = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - yz - z x) = 9 (29 - 26) = 27

.

Answer: A) 27

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