Find HCF of 8x^3 + 4x^2 + 2x, 16x^4 + 4x^2 + 1 and 8x^3 - 1

You are on right track, Rames. If u got stuck in 1st expression, leave some space and start solving other expression.

In this situation, we can't solve any further than what u have solved in 1st expression. I did the 2nd expression and got the common result from both expression. 3rd expression also gives the common expression.

1st expression:
= 8x³ + 4x² + 2x
= 2x(4x² + 2x + 1)

2nd expression:
= 16x⁴ + 4x² + 1
= (4x²)² + (2x)² + 1
= (4x²)² + 1² + (2x)²
= (4x² + 1)² - 8x² + 4x²
= (4x² + 1)² - (2x)²
= (4x² + 1 + 2x)(4x² + 1 - 2x)
= (4x² + 2x + 1)(4x² - 2x + 1)

3rd expression:
= 8x³ - 1
= (2x)³ - 1³
= (2x - 1)(4x² + + 2x + 1)

∴ HCF = highest common factor = 4x² + + 2x + 1

Here is the video expression: