How do you factor $(A-B)^3 - B^3$ ?

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Answer 1 · 2015-05-31T13:16:09

This is a difference of cubes, so we can use the identity:

$P^3-Q^3 = (P-Q)(P^2+PQ+Q^2)$ ....

$(A-B)^3 - B^3$

$=((A-B)-B)((A-B)^2+(A-B)B +B^2)$

$=(A-2B)(A^2-2AB+B^2+AB-B^2+B^2)$

$=(A-2B)(A^2-AB+B^2)$

This has no simpler factors with real coefficients.

How do you factor (A-B)^3 - B^3(A-B)^3 - B^3?