Which of the following is a factor of (x + y)3 - (x3 + y3 )
a. x² + y² + 2xy
b. x² + y² - xy
c. xy²
d. 3xy

Solution:

It is given that

(x + y)3 - (x3 + y3 )

Using the algebraic identity (a + b)3 = a3 + b3 + 3ab (a + b)

= x3 + y3 + 3xy (x + y) - x3 - y3

By further simplification

= 3xy (x + y)

Therefore, 3xy is a factor of (x + y)3 - (x3 + y3).

✦ Try This: If x - 1 is a factor of the polynomial 7x² + kx, then the value of k is

Consider p(x) = 7x² + kx

As x - 1 is a factor of p(x)

p(1) = 0

Substituting x = 1

7(1)² + k(1) = 0

By further calculation

7 + k = 0

k = -7

Therefore, the value of k is -7.

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

NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 17

Which of the following is a factor of (x + y)3 - (x3 + y3 )? a. x² + y² + 2xy, b. x² + y² - xy, c. xy², d. 3xy

Summary:

A factor is a number that divides the given number without any remainder. 3xy is a factor of (x + y)3 - (x3 + y3)

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