Simplify (a-b) (a²+ab+b²)
Answers
Answer:
Why do we simplify (a+b) ² to a²+2ab+b², and not a²+b²?
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Because it's wrong. When doing math with variables, a simple check with substituting real numbers helps. If it fails once, then you didn't solve it correctly.
If: (a+b)^2 = a^2 + b^2
Then this must be true: (1 + 3)^2 = 1^2 + 3^2
Check it: (1+3)^2 = 4^2 = 16 ----> 1^2 + 3^2 = 1 + 9 = 10
16 does not equal 10, so (a+b)^2 = a^2 + b^2 is not a valid solution.
It basically comes back to improper understanding of an exponent.
(a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ba + b^2 = a^2+ 2ab + b^2
For clarity, an exponent cannot be distributed through addition as you are attempting to do. Exponents are just short hand for multiplying something by itself, and you must do the full multiplication. I hate the word "simplify". You are converting it from one form to another. Which form is "simpler" is a matter of opinion, a fact that many math books seem to forget.
Answer:
a(a^2+ab+b^2)-b(a^2+ab+b^2) = a^3++a^2b+ab^2-a^2b-ab^2-b^3 =a^3-b^3 (ans)