If a + b + c = 0, then a³ + b³ + c³ is equal to
a. 0
b. abc
c. 3abc
d. 2abc

Solution:

We know that

a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - bc - ca - ab)

It is given that

a + b + c = 0

So we get

a³ + b³ + c³ - 3abc = 0

a³ + b³ + c³ = 3abc

Therefore, a³ + b³ + c³ is equal to 3abc.

✦ Try This: If 25x² - b = (5x + 1/2) (5x - 1/2), then the value of b is

It is given that

25x² - b = (5x + 1/2) (5x - 1/2)

Using the algebraic identity a² - b² = (a + b) (a - b)

25x² - b = 25x² - 1/4

Equating from both sides

b = 1/4

Therefore, the value of b is 1/4.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

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NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 21

If a + b + c = 0, then a³ + b³ + c³ is equal to a. 0, b. abc, c. 3abc, d. 2abc

Summary:

Addition of polynomials is one of the basic operations that we use to increase or decrease the value of polynomials. If a + b + c = 0, then a³ + b³ + c³ is equal to 3abc

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☛ Related Questions:

• Which of the following is a factor of (x + y)3 - (x3 + y3 )? a. x² + y² + 2xy, b. x² + y² - xy, c. x . . . .
• The coefficient of x in the expansion of (x + 3)3 is a. 1, b. 9, c. 18, d. 27
• If x/y + y/x = -1, (x, y ≠ 0), the value of x3 - y3 is a. 1, b. -1, c. 0, d. 1/2