Question

Factorise: 16c⁴ − 1
please answer fast and correct ​

Answer 1

Solution:

Topic: Factorisation.

We have to factorise - 16c⁴ - 1.

• This problem can be solved using identity - a² - b² = (a + b)(a - b)
• We have to express the given polynomial as a difference of two squares and then using the above mentioned identity, we will factorise.

Solution:

16c⁴ - 1 can be written as,

= (4c²)² - (1)²

Applying the identity here, we get,

= (4c² + 1)(4c² - 1)

4c² - 1 can be written as,

= (2c)² - (1)²

Applying the same identity again, we get,

= (2c + 1)(2c - 1)

So,

→ 4c² - 1 = (2c + 1)(2c - 1)

So,

16c⁴ - 1

= (4c² + 1)(4c² - 1)

= (4c² + 1)(2c + 1)(2c - 1) which is our required answer.

Answer:

• (4c² + 1)(2c + 1)(2c - 1)

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