# Find the HCF from a^3 - a^2 + a - 1 and 2a^3 - a^2 + a - 2

Hello my friend! How can i solve this?

1st expression:

= a^{3} - a^{2} + a - 1

= ...?

Pls help. Thank u. Nice day!

Go to main content# Find the HCF from a^3 - a^2 + a - 1 and 2a^3 - a^2 + a - 2

Hello my friend! How can i solve this?

1st expression:

= a^{3} - a^{2} + a - 1

= ...?

Pls help. Thank u. Nice day!

Hello friend! It's pretty easy. U just need to practice more, and I guess u r on right track.

For this question, in the 1st expression, we just need to take a common.

For 2nd expression, it's lil tricky. If u take the common from first 2 expression, it will not get solved. U need to take the 1st & last expression and take the common. Below is the solution.

1st expression:

= a^{3} - a^{2} + a - 1

= a^{2}(a - 1) + 1(a - 1)

= (a - 1)(a^{2} + 1)

2nd expression:

= 2a^{3} - a^{2} + a - 2

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

= 2(a - 1)(a^{2} + a + 1) - a(a - 1)

= (a - 1){2(a^{2} + a + 1) - a}

Here, common factor from both expression is (a - 1). So our answer is (a - 1)

Video explanation: