Use a suitable identity to evaluate 99³.

970299. Write 99 = 100 − 1 and use (a − b)³ = a³ − 3a²b + 3ab² − b³: 99³ = 1000000 − 3(10000)(1) + 3(100)(1) − 1 = 1000000 − 30000 + 300 − 1 = 970299.

Use a suitable identity to evaluate $9 9^{3}$ .

Class 9PolynomialsPolynomials

A970299
B999999
C970199
D970301

Step-by-Step Solution

Write 99 = 100 − 1 and use

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} : 9 9^{3} = 1000000 - 3 (10000) (1) + 3 (100) (1) - 1 = 1000000 - 30000 + 300 - 1 = 970299

Answer: A) 970299

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 a suitable identity to evaluate 993.

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 a suitable identity to evaluate $9 9^{3}$ .