# Which of the following is a factor of (x + y)^{3} - (x^{3} + y^{3} )

a. x² + y² + 2xy

b. x² + y² - xy

c. xy²

d. 3xy

**Solution:**

It is given that

(x + y)^{3} - (x^{3} + y^{3} )

Using the algebraic identity (a + b)^{3} = a^{3} + b^{3} + 3ab (a + b)

= x^{3} + y^{3} + 3xy (x + y) - x^{3} - y^{3}

By further simplification

= 3xy (x + y)

Therefore, 3xy is a factor of (x + y)^{3} - (x^{3} + y^{3}).

**✦ 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} - (x^{3} + y^{3} )? 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} - (x^{3} + y^{3})

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