Use the identity for a³ + b³ + c³ − 3abc to evaluate 2³ + 3³ + 4³ − 3(2)(3)(4).

27. The identity gives (a + b + c)(a² + b² + c² − ab − bc − ca) = (2 + 3 + 4)(4 + 9 + 16 − 6 − 12 − 8) = 9 × 3 = 27. Direct check: 8 + 27 + 64 − 72 = 99 − 72 = 27.

Use the identity for $a^{3} + b^{3} + c^{3} - 3$ $ab c$ to evaluate $2^{3} + 3^{3} + 4^{3} - 3 (2) (3) (4)$ .

Class 9PolynomialsPolynomials

Step-by-Step Solution

The identity gives

(a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a) = (2 + 3 + 4) (4 + 9 + 16 - 6 - 12 - 8) = 9 \times 3 = 27

. Direct check: 8 + 27 + 64 − 72 = 99 − 72 = 27.

Answer: D) 27

Key idea: Naming polynomials by terms and degree

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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Use the identity for a3+b3+c3−3abc to evaluate 23+33+43−3(2)(3)(4).

Step-by-Step Solution

Key idea: Naming polynomials by terms and degree

Master this chapter in 30 minutes a day.

More Class 9 Polynomials practice

Use the identity for $a^{3} + b^{3} + c^{3} - 3$ $ab c$ to evaluate $2^{3} + 3^{3} + 4^{3} - 3 (2) (3) (4)$ .