If a + b = 10 and ab = 21, find a³ + b³.

370. From (a + b)³ = a³ + b³ + 3ab(a + b) we get a³ + b³ = (a + b)³ − 3ab(a + b) = 10³ − 3(21)(10) = 1000 − 630 = 370. Check: a and b are 3 and 7, and 27 + 343 = 370.

If $a + b = 10$ and $ab = 21$ , find $a^{3} + b^{3}$ .

Class 9PolynomialsPolynomials

A1630
B790
C370
D1000

Step-by-Step Solution

From

(a + b)^{3} = a^{3} + b^{3} + 3 ab (a + b)

we get

a^{3} + b^{3} = (a + b)^{3} - 3 ab (a + b) = 1 0^{3} - 3 (21) (10) = 1000 - 630 = 370

. Check: a and

b

are 3 and 7, and 27 + 343 = 370.

Answer: C) 370

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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If a+b=10 and ab=21, find a3+b3.

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

If $a + b = 10$ and $ab = 21$ , find $a^{3} + b^{3}$ .