MP Board · Class 9 · Mathematics · PolynomialsIf $x + y + z = 0$, then $x^3 + y^3 + z^3$ is equal to:
Step-by-Step Solution
Using the algebraic identity $x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)$,\nwhen $x + y + z = 0$, the right side becomes $0$. Therefore, $x^3 + y^3 + z^3 = 3xyz$.
Detailed Options Breakdown
Option : 0
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 1: $xyz$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 2: $3xyz$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: $(x + y + z)^3$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
💡 Study Guide: This question tests core syllabus concepts from Polynomials. For formulas, key summaries, and mock exam reference guides, read the full Polynomials Revision Notes.