I am having problems understand these concepts which I got from an AMaths 'O' Level Revision Guide. I have used this concepts for question. (Copy but do not understand).
a = alpha
b = beta
1) a³ + b³ = (a + b)(a² - ab + b²) ----- I do not understand how is this gotten from a³ + b³
= (a + b)[ (a + b)² - 3ab ----- understand and able to continue on.
2) a³ - b³ = (a - b)(a² + ab + b²) ----- i do not understand how this is gotten from a³ - b³
= (a - b)[ (a + b)² -ab ] ------ understand and able to continue on.
PS: If its too hard to explain, then never mind. Thanks for your help!
Hi,
Both are standard results, which can be verified by means of expanding.
I feel that it is too difficult and therefore unreasonable to expect a student to know these results at O-level.
These facts are suited at A-level and beyond in my view. Thanks!
P.S. In my daily encounters with mathematics, I do not use these results even :P
Cheers,
Wen Shih
Thanks, Wen Shih