If a + b + c = 0, then a³ + b³ + c³ equals which of the following?

3abc. The identity a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca). When a + b + c = 0, the right side is 0, so a³ + b³ + c³ = 3abc.

If $a + b + c = 0$ , then $a^{3} + b^{3} + c^{3}$ equals which of the following?

Class 9PolynomialsPolynomials

The identity

a^{3} + b^{3} + c^{3} - 3 ab c = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a)

. When

a + b + c = 0

, the right side is 0, so

a^{3} + b^{3} + c^{3} = 3 ab c

Answer: A) 3abc

By number of terms:
- **Monomial**: 1 term (e.g.

5 x^{3}

)
- **Binomial**: 2 terms (e.g.

x^{2} + 3

)
- **Trinomial**: 3 terms (e.g.

x^{2} + 2 x + 1

)

By degree:
- **Linear** (degree 1):

3 x - 5

- **Quadratic** (degree 2):

x^{2} - 4

- **Cubic** (degree 3):

2 x^{3} + x - 1

- **Biquadratic** (degree 4):

x^{4} + 1

A polynomial can fit multiple categories.

5 x^{3}

is both a monomial and a cubic.

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