nuance or exception to the rule, need clarification

[bobisaka]

Hi all,

So for this cube of differences:

x^3 - 2^3

Using the formula a^3 - b^3 = (a - b) (a^2 + ab + b^2), the answer should be (x -2) (x^2 + 2x + 2^2)

However, my question is that if i were to strictly follow the formula it would equal (x-2) (x^2 +x2 + 2^2), since a = x and b = 2.

I know we don't write coefficient/variables in such a way, so does that mean this is an exception to the rule of the formula and is this a nuance that I should disregard?

 

[lev888]

Question:

View attachment 18299

Answer:
View attachment 18300


I can solve the denominator but am stuck at the factoring the numerator specifically the first part x^3 - 8. Cannot move to the next step..

Tried looking for examples in the text book, but can't find anything with a co-efficient of 1.

Look up difference of cubes.

 

[bobisaka]

Look up difference of cubes.

Yeah, sorry was in the process of editing my question..That was the bit i found out..


How am I suppose to retain all these formulas.. I am not a student, but study in my spare time that i have..

 

[lev888]

Hi all,

So for this cube of differences:

x^3 - 2^3

Using the formula a^3 - b^3 = (a - b) (a^2 + ab + b^2), the answer should be (x -2) (x^2 + 2x + 2^2)

However, my question is that if i were to strictly follow the formula it would equal (x-2) (x^2 +x2 + 2^2), since a = x and b = 2.

I know we don't write coefficient/variables in such a way, so does that mean this is an exception to the rule of the formula and is this a nuance that I should disregard?

2x = x2
Please look up commutative property of multiplication.

 

[bobisaka]

thanks, yes i remember that property now that you mentioned it.