Question: Find the HCF of the following expressions: a³ -1, and a⁴ +a² +1.

Solution:
Given,

1st expression: a³ -1
= a³ -1³
= (a-1)(a² +a +1)

2nd expression: a⁴ +a² +1
= (a²)² +1² +a²
= (a² +1)² -2a² +a²
= (a² +1)² - a²
= (a² +1)² - (a)²
= (a² +a +1)(a² -a +1)

Now,

Highest Common Factor (H.C.F.) = common factors only
= (a² +a +1)

Related Notes and Solutions:

Here is the Facebook link to the solution of this question in image. 

Here is the Website link to the guide of solving HCF and LCM.

#SciPiPupil