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

I am stuck in first expression. I'm not sure how to solve further. Pls help

1st expression = 8x^{3} + 4x^{2} + 2x

= 2x(4x^{2} + 2x + 1)

Go to main content# Find HCF of 8x^3 + 4x^2 + 2x, 16x^4 + 4x^2 + 1 and 8x^3 - 1

I am stuck in first expression. I'm not sure how to solve further. Pls help

1st expression = 8x^{3} + 4x^{2} + 2x

= 2x(4x^{2} + 2x + 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:

= 8x^{3} + 4x^{2} + 2x

= 2x(4x^{2} + 2x + 1)

2nd expression:

= 16x^{4} + 4x^{2} + 1

= (4x^{2})^{2} + (2x)^{2} + 1

= (4x^{2})^{2} + 1^{2} + (2x)^{2}

= (4x^{2} + 1)^{2} - 8x^{2} + 4x^{2}

= (4x^{2} + 1)^{2} - (2x)^{2}

= (4x^{2} + 1 + 2x)(4x^{2} + 1 - 2x)

= (4x^{2} + 2x + 1)(4x^{2} - 2x + 1)

3rd expression:

= 8x^{3} - 1

= (2x)^{3} - 1^{3}

= (2x - 1)(4x^{2} + + 2x + 1)

∴ HCF = highest common factor = 4x^{2} + + 2x + 1

Here is the video expression: