# One of the factors of (25x² - 1) + (1 + 5x)² is

a. 5 + x

b. 5 - x

c. 5x - 1

d. 10x

**Solution:**

It is given that

(25x² - 1) + (1 + 5x)²

Using the algebraic identity (a + b)² = a² + b² + 2ab

= 25x² - 1 + 1 + 25x² + 10x

By further calculation

= 50x² + 10x

Taking out the common term

= 10x (5x + 1)

Therefore, one of the factors is 10x.

**✦ Try This: **One of the factors of (16x² - 1) + (1 + 4x)² is a.4x - 1, b. 4 - x, c. 4 + x, d. 8x

It is given that

(16x² - 1) + (1 + 4x)²

Using the algebraic identity (a + b)² = a² + b² + 2ab

= 16x² - 1 + 1 + 16x² + 8x

By further calculation

= 32x² + 8x

Taking out the common term

= 8x (4x + 1)

Therefore, one of the factors is 8x.

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

**NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 14**

## One of the factors of (25x² - 1) + (1 + 5x)² is a. 5 + x, b. 5 - x, c. 5x - 1, d. 10x

**Summary:**

Factoring Polynomials means decomposing the given polynomial into a product of two or more polynomials using prime factorization. One of the factors of (25x² - 1) + (1 + 5x)² is 10x

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