Question

Please help work me through this ASAP! *MEDALS*


A^3 + b^3 = (a+b)(a^2-2ab+b^2)

Answer 1

o a^3+b^3 does NOT equal (a+b)(a+b)^2. For example, if a=b=1, then a^3+b^3 = 1 + 1 = 2 but (a+b)(a+b)^2 = (1+1)(1+1)^2 = (2)(2^2) = 8.

It has to be a minus in the right side, since when you multiply out the right side you need things to cancel so there must be OPPOSITE signs in the first factor (a+b) and the second factor (a^2-ab+b^2) to make that cancellation happen.

Similarly, in a^3-b^3=(a-b)(a^2+ab+b^2), you have to have OPPOSITE signs in the two factors on the right side or there will be no cancellation.

Answer 2

Okay.. I think I get the jist. But I'm more visual, so could you work me through step by step?

Answer 3

a+b)^3 is the one that equals (a+b)(a+b)^2 not a^3+b^3

if you try to multiply (a+b) times each variable in the second brackets it'll be (a+b)(a^2) + (a+b)(-ab) + (a+b)(b^2) which equals:
a^3+a^2b - a^2b - ab^2 + ab^2 + b^3
cross the corresponding positive and negative variables to end up with a^3 + b^3
so a^3+b^3=(a+b)(a^2-ab+b^2) is correct hope this helps :)

Answer 4

Thank you!!

Answer 5

your welcome !