Yet another simple factorizing question

[alpha01]

[SOLVED] yet another simple factorizing question..

I won't re-write the full question, just one line on the numerator:

from the solutions, (a + 1)^2 − (a − 1)^2 factorizes to:

((a + 1) − (a − 1))((a + 1) + (a − 1))

I can see that this is just another form of:

(a + 1)(a + 1) - (a - 1)(a - 1)

but why is the former, and not the later used?

does it make it easier to go to the next step to complete factorization process?

If so please explain why.

 

[cristo]

does it make it easier to go to the next step to complete factorization process?

Well, it's going to depend on what the question asks next!

 

[alpha01]

the solution continues on like this:

= (a + 1 − a + 1)(a + 1 + a − 1)

= 4a

(the question is to factorize.. i don't know what you mean by "what does it ask next")

 

[cristo]

Ok, I think I get what you mean now. Well, your first expression is in the form x^2-y^2, which is a difference of two squares. We know that the factorisation of a difference of two squares is (x+y)(x-y); it just turns out that in this case the expression simplifies further.

The second expression you give in your first post is not a factorisation of (a+1)^2-(a-1)^2, but is an expansion.

 

[alpha01]

thank you, understood