Quandaries and Queries


Why does

"a"cubed minus "b"cubed equal (a-b) times
("a"squared plus "ab" plus "b"squared)?

I know this is a formula, but why is it true?




Hi Denise,

Factoring is often a matter of looking at an expression and seeing a pattern, or recognizing something you have seen before. For example the fact that I know twenty-four is six times four is that when I learned my times tables I learned that

6 4 = 24

and I can read it backwards to get

24 = 6 4.

The same is true for a3 - b3 . I know that if I multiply

(a - b)(a2 + ab + b2)

I get

(a - b)(a2 + ab + b2)
= a3 + a2b + ab2 - a2 - ab2 - b3
= a3 - b3

and I can read it backwards to get

a3 - b3 = (a - b)(a2 + ab + b2)



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